Fluctuations in classical sum rules.
Elton, John R; Lakshminarayan, Arul; Tomsovic, Steven
2010-10-01
Classical sum rules arise in a wide variety of physical contexts. Asymptotic expressions have been derived for many of these sum rules in the limit of long orbital period (or large action). Although sum-rule convergence may well be exponentially rapid for chaotic systems in a global phase-space sense with time, individual contributions to the sums may fluctuate with a width which diverges in time. Our interest is in the global convergence of sum rules as well as their local fluctuations. It turns out that a simple version of a lazy baker map gives an ideal system in which classical sum rules, their corrections, and their fluctuations can be worked out analytically. This is worked out in detail for the Hannay-Ozorio sum rule. In this particular case the rate of convergence of the sum rule is found to be governed by the Pollicott-Ruelle resonances, and both local and global boundaries for which the sum rule may converge are given. In addition, the width of the fluctuations is considered and worked out analytically, and it is shown to have an interesting dependence on the location of the region over which the sum rule is applied. It is also found that as the region of application is decreased in size the fluctuations grow. This suggests a way of controlling the length scale of the fluctuations by considering a time dependent phase-space volume, which for the lazy baker map decreases exponentially rapidly with time.
NASA Astrophysics Data System (ADS)
Dominguez, C. A.
2013-08-01
A general, and very basic introduction to QCD sum rules is presented, with emphasis on recent issues to be described at length in other papers in this issue. Collectively, these papers constitute the proceedings of the International Workshop on Determination of the Fundamental Parameters of QCD, Singapore, March 2013.
Exact sum rules for inhomogeneous strings
Amore, Paolo
2013-11-15
We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order N may be obtained in terms of a diagrammatic expansion, with (N−1)!/2 independent diagrams. These sum rules are used to derive upper and lower bounds to the energy of the fundamental mode of an inhomogeneous string; we also show that it is possible to improve these approximations taking into account the asymptotic behavior of the spectrum and applying the Shanks transformation to the sequence of approximations obtained to the different orders. We discuss three applications of these results. -- Highlights: •We derive an explicit expression for the sum rules of an inhomogeneous string. •We obtain a diagrammatic representation for the sum rules of a given order. •We obtain precise bounds on the lowest eigenvalue of the string.
Sum rule of the correlation function
Maj, Radoslaw; Mrowczynski, Stanislaw
2005-04-01
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of two particles, is derived and checked to see how it works in practice. The sum rule is shown to be trivially satisfied by free particle pairs. We then analyze three different systems of interacting particles: neutron and proton pairs in the s-wave approximation, the so-called hard spheres with phase shifts taken into account up to l=4, and finally, the Coulomb system of two charged particles.
Nuclear magnetic moments and related sum rules
Bentz, Wolfgang; Arima, Akito
2011-05-06
We first review the history and our present understanding of nuclear magnetic moments and Gamow-Teller transitions, with emphasis on the roles of configuration mixing and meson exchange currents. Then we discuss the renormalization of the orbital g-factor in nuclei, and its relation to the E1 sum rule for photoabsorption and the M1 sum rule for the scissors mode of deformed nuclei.
Quasielastic (e,e') sum rule saturation
C. R. Chinn; A. Picklesimer; Wally Van Orden
1989-09-01
A microscopic Green's function doorway formalism is used to study Coulomb sum rule saturation in inclusive quasielastic electron scattering as a function of momentum transfer. Form factor, kinematical restriction, and final-state interaction effects on the approach to saturation are examined in detail, as are the roles of nonhermiticity, energy dependence, and the analytic behavior of the final-state interactions. The implications of relativistic kinematics and dynamics for the approach to saturation at not-too-high values of the momentum transfer are assessed. Because the pair production of relativistic treatments destroys the asymptotic nature of the nonrelativistic Coulomb sum rule, the degree to which a regime of validity can be expected for this sum rule, and its location, is considered. The breakdown of the sum rule as the momentum transfer increases is also examined. Similar theoretical studies of an analogous nonrelativistic transverse sum in its saturation region are developed as well. Theoretical predictions are compared with the experimental data for {sup 40}Ca both directly and using a variety of theoretical prescriptions and limits. Neutron knockout contributions and associated uncertainties due to ambiguity in the free neutron form factors are examined.
Coulomb sum rule in the quasielastic region
Kim, K. S.; Yu, B. G.; Cheoun, M. K.
2006-12-15
Within a relativistic single particle model, we calculate the Coulomb sum rule of inclusive electron scattering from {sup 40}Ca and {sup 208}Pb in the quasielastic region. Theoretical longitudinal and transverse structure functions are extracted for three-momentum transfers from 300 to 500 MeV/c and compared with the experimental data measured at Bates and Saclay. We find that there is no drastic suppression of the longitudinal structure function and that the Coulomb sum rule depends on the nucleus in our theoretical model.
Generalized Sum Rules of the Nucleon
NASA Astrophysics Data System (ADS)
Gorshteyn, Mikhail; Szczepaniak, Adam
2008-10-01
We consider doubly virtual Compton scattering (VVCS) off the nucleon with the photon virtualities q1^2=q2^2=-Q^2 and formulate the low energy theorem (LET) for this process. We show that the LET can only be defined at finite momentum transfer t=-2Q^2 which is at variance with existing studies in the literature. Combining LET with dispersion relations for the forward VVCS amplitude, we obtain the new, correct version of the generalized sum rules of the nucleon that state a correspondence between the low energy constants of VVCS and the moments of the DIS structure functions. We notice that the t-channel unitarity is necessary to translate the forward dispersion relations to the low energy limit. This approach leads to a substantial modification of the generalized GDH sum rule at finite Q^2 that undergoes extensive studies at JLab. For the spin-independent VVCS amplitude, the new sum rule for the generalized magnetic susceptibility β(Q^2) is obtained. Our approach provides a consistent, Lorentz invariant formulation of LET for the most general VVCS process that removes inconsistencies that stain the previous studies of the generalized polarizabilities of virtual Compton scattering and the generalized sum rules of the nucleon.
Kaon distribution amplitude from QCD sum rules
Khodjamirian, A.; Mannel, Th.; Melcher, M.
2004-11-01
We present a new calculation of the first Gegenbauer moment a{sub 1}{sup K} of the kaon light cone distribution amplitude. This moment is determined by the difference between the average momenta of strange and nonstrange valence quarks in the kaon. To calculate a{sub 1}{sup K}, QCD sum rule for the diagonal correlation function of local and nonlocal axial-vector currents is used. Contributions of condensates up to dimension six are taken into account, including O({alpha}{sub s})-corrections to the quark-condensate term. We obtain a{sub 1}{sup K}=0.05{+-}0.02, differing by the sign and magnitude from the recent sum rule estimate from the nondiagonal correlation function of pseudoscalar and axial-vector currents. We argue that the nondiagonal sum rule is numerically not reliable. Furthermore, an independent indication for a positive a{sub 1}{sup K} is given, based on the matching of two different light cone sum rules for the K{yields}{pi} form factor. With the new interval of a{sub 1}{sup K}, we update our previous numerical predictions for SU(3)-violating effects in B{sub (s)}{yields}K form factors and charmless B decays.
Systematics of strength function sum rules
Johnson, Calvin W.
2015-08-28
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expectssum rules to evolve with excitation energy. Moreover, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
Systematics of strength function sum rules
Johnson, Calvin W.
2015-08-28
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens,more » violation of the generalized Brink–Axel hypothesis is unsurprising: one expectssum rules to evolve with excitation energy. Moreover, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).« less
Limiting law excess sum rule for polyelectrolytes
NASA Astrophysics Data System (ADS)
Landy, Jonathan; Lee, YongJin; Jho, YongSeok
2013-11-01
We revisit the mean-field limiting law screening excess sum rule that holds for rodlike polyelectrolytes. We present an efficient derivation of this law that clarifies its region of applicability: The law holds in the limit of small polymer radius, measured relative to the Debye screening length. From the limiting law, we determine the individual ion excess values for single-salt electrolytes. We also consider the mean-field excess sum away from the limiting region, and we relate this quantity to the osmotic pressure of a dilute polyelectrolyte solution. Finally, we consider numerical simulations of many-body polymer-electrolyte solutions. We conclude that the limiting law often accurately describes the screening of physical charged polymers of interest, such as extended DNA.
Symmetries, sum rules and constraints on effective field theories
NASA Astrophysics Data System (ADS)
Bellazzini, Brando; Martucci, Luca; Torre, Riccardo
2014-09-01
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the scattering amplitudes in the IR to total cross sections integrated all the way up to the UV. Exploiting the group structure of the symmetry, we systematically determine all the independent sum rules and positivity conditions on the expansion coefficients. For effective field theories the amplitudes in the IR are calculable and hence the sum rules set constraints on the parameters of the effective Lagrangian. We clarify the impact of gauging on the sum rules for Goldstone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for WW-scattering, composite Higgs models, and chiral perturbation theory. Certain sum rules based on custodial symmetry and its extensions provide constraints on the Higgs boson coupling to the electroweak gauge bosons.
Electromagnetic response of superconductors and optical sum rule
NASA Astrophysics Data System (ADS)
Karakozov, A. E.; Maksimov, E. G.; Dolgov, O. V.
2002-10-01
The interrelation between the condensation energy and the optical sum rules have been investigated. It has been shown that the so called 'partial' sum rule violation is related mainly to a temperature dependence of the relaxation rate rather than to the appearance of superconductivity itself. Moreover, we demonstrate that the experimental data on the temperature dependence of the optical sum rule can be explained rather well by accounting for the strong electron-phonon interaction.
Tuning sum rules with window functions for optical constant evaluation
NASA Astrophysics Data System (ADS)
Rodríguez-de Marcos, Luis V.; Méndez, José A.; Larruquert, Juan I.
2016-07-01
Sum rules are a useful tool to evaluate the global consistency of a set of optical constants. We present a procedure to spectrally tune sum rules to evaluate the local consistency of optical constants. It enables enhancing the weight of a desired spectral range within the sum-rule integral. The procedure consists in multiplying the complex refractive index with an adapted function, which is named window function. Window functions are constructed through integration of Lorentz oscillators. The asymptotic decay of these window functions enables the derivation of a multiplicity of sum rules akin to the inertial sum rule, along with one modified version of f-sum rule. This multiplicity of sum rules combined with the free selection of the photon energy range provides a double way to tune the spectral contribution within the sum rule. Window functions were applied to reported data of SrF2 and of Al films in order to check data consistency over the spectrum. The use of window functions shows that the optical constants of SrF2 are consistent in a broad spectrum. Regarding Al, some spectral ranges are seen to present a lower consistency, even though the standard sum rules with no window function did not detect inconsistencies. Hence window functions are expected to be a helpful tool to evaluate the local consistency of optical constants.
Second sum rule for the hot plasma permittivity
Bobrov, V. B.; Mendeleyev, V. Ya.; Skovorod'ko, S. N.; Trigger, S. A.
2011-02-15
Based on linear response theory, Kramers-Kronig relations, and diagram techniques of perturbation theory, it is shown that the second sum rule is satisfied for hot plasma permittivity. An explicit analytical expression for the second sum rule in the limit of weak nonideality is derived.
Charmonium sum rules applied to a holographic model
Hohler, Paul M.
2011-01-15
The heavy-quark QCD sum rules are applied to a model of charmonium based upon the gauge/gravity duality. We find that there is strong agreement between the moments of the polarization function calculated from the holographic model and the experimental data suggesting that the model is consistent with the heavy-quark QCD sum rules at zero temperature.
Photo-absorption sum rules σ-1 in different environments
NASA Astrophysics Data System (ADS)
Gerasimov, S. B.
2016-02-01
Combining the spin-dependent dispersion GDH-sum rule, the iso-vector, photo-excitation states projecting Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (or generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector.
Testing atmospheric mixing sum rules at precision neutrino facilities
NASA Astrophysics Data System (ADS)
Ballett, Peter; King, Stephen F.; Luhn, Christoph; Pascoli, Silvia; Schmidt, Michael A.
2014-01-01
We study the prospects for testing classes of atmospheric mixing sum rules at precision neutrino facilities. Such sum rules, which correlate the atmospheric mixing angle θ23 with the recently measured reactor angle θ13 and the cosine of the oscillation phase δ, are predicted by a variety of semidirect models based on discrete family symmetry classified in terms of finite von Dyck groups. We perform a detailed simulation of the performance of the next generation of oscillation experiments, including the wideband superbeam and low-energy neutrino factory proposals, and compare their discriminating power for testing atmospheric mixing sum rules.
Quark mixing sum rules and the right unitarity triangle
Antusch, Stefan; Spinrath, Martin; King, Stephen F.; Malinsky, Michal
2010-02-01
In analogy with the recently proposed lepton mixing sum rules, we derive quark mixing sum rules for the case of hierarchical quark mass matrices with 1-3 texture zeros, in which the separate up and down-type 1-3 mixing angles are approximately zero, and V{sub ub} is generated from V{sub cb} as a result of 1-2 up-type quark mixing. Using the sum rules, we discuss the phenomenological viability of such textures, including up to four texture zeros, and show how the right-angled unitarity triangle, i.e., {alpha}{approx_equal}90 deg., can be accounted for by a remarkably simple scheme involving real mass matrices apart from a single element being purely imaginary. In the framework of grand unified theories, we show how the quark and lepton mixing sum rules may combine to yield an accurate prediction for the reactor angle.
Charm and bottom hadronic form factors with QCD sum rules
Bracco, M. E.; Rodrigues, B. O.; Cerqueira, A. Jr.
2013-03-25
We present a brief review of some calculations of form factors and coupling constants in vertices with charm and bottom mesons in the framework of QCD sum rules. We first discuss the motivation for this work, describing possible applications of these form factors to charm and bottom decays processes. We first make a summarize of the QCD sum rules method. We give special attention to the uncertainties of the method introducing by the intrinsic variation of the parameters. Finally we conclude.
Sum Rules, Classical and Quantum - A Pedagogical Approach
NASA Astrophysics Data System (ADS)
Karstens, William; Smith, David Y.
2014-03-01
Sum rules in the form of integrals over the response of a system to an external probe provide general analytical tools for both experiment and theory. For example, the celebrated f-sum rule gives a system's plasma frequency as an integral over the optical-dipole absorption spectrum regardless of the specific spectral distribution. Moreover, this rule underlies Smakula's equation for the number density of absorbers in a sample in terms of the area under their absorption bands. Commonly such rules are derived from quantum-mechanical commutation relations, but many are fundamentally classical (independent of ℏ) and so can be derived from more transparent mechanical models. We have exploited this to illustrate the fundamental role of inertia in the case of optical sum rules. Similar considerations apply to sum rules in many other branches of physics. Thus, the ``attenuation integral theorems'' of ac circuit theory reflect the ``inertial'' effect of Lenz's Law in inductors or the potential energy ``storage'' in capacitors. These considerations are closely related to the fact that the real and imaginary parts of a response function cannot be specified independently, a result that is encapsulated in the Kramers-Kronig relations. Supported in part by the US Department of Energy, Office of Nuclear Physics under contract DE-AC02-06CH11357.
Sum rule for response function in nonequilibrium Langevin systems
NASA Astrophysics Data System (ADS)
Yuge, Tatsuro
2010-11-01
We derive general properties of the linear-response functions of nonequilibrium steady states in Langevin systems. These correspond to extension of the results which were recently found in Hamiltonian systems [A. Shimizu and T. Yuge, J. Phys. Soc. Jpn. 79, 013002 (2010)10.1143/JPSJ.79.013002]. We discuss one of the properties, the sum rule for the response function, in particular detail. We show that the sum rule for the response function of the velocity holds in the underdamped case, whereas it is violated in the overdamped case. This implies that the overdamped Langevin models should be used with great care. We also investigate the relation of the sum rule to an equality on the energy dissipation in nonequilibrium Langevin systems, which was derived by Harada and Sasa.
Vector mesons at finite temperature and QCD sum rules
Kwon, Youngshin; Weise, Wolfram; Sasaki, Chihiro
2010-06-15
Finite energy sum rules for vector and axial-vector currents are derived in a thermal medium to provide constraints for the spectral behavior of rho and a{sub 1} mesons at nonvanishing temperature and hence to study the tendency toward chiral symmetry restoration. The parity-mixing ansatz for the rho and a{sub 1} spectra, including finite widths, is investigated as a function of temperature. Characteristic differences between vector and axial-vector channels are discussed with regard to the implementation of the chiral-symmetry-breaking scale, 4pi times the pion decay constant, in the sum-rule approach.
Gravitons and the Drell-Hearn-Gerasimov sum rule
NASA Astrophysics Data System (ADS)
Goldberg, H.
2000-01-01
One-loop diagrams containing a graviton provide a finite contribution to the anomalous magnetic moment al of a lepton, whether or not the graviton propagates in n large extra compact dimensions. In the present work, the tree graph photoproduction of a graviton, integrated up to an arbitrary cutoff, is shown to violate the Drell-Hearn-Gerasimov sum rule for al2. The possibility of resurrecting the sum rule from high energy contributions originating in string excitations is discussed in a qualitative manner, and various problems associated with such a program are pointed out.
Jackiw-Johnson sum rule for dynamical symmetry breaking
Appelquist, T.; Takeuchi, T. ); Einhorn, M.B. ); Wijewardhana, L.C.R. )
1990-05-15
We reconsider the Jackiw-Johnson sum rule relating the vector-boson masses (or Goldstone-boson decay constants) to the interactions of the fermions which condense. We show that the counterterm can be simplified to remove all reference to chiral-symmetry breaking, producing a much simpler formula involving no derivatives of the fermion self-energy. This is useful for applications to QCD and technicolor. In the process, we also generalize the sum rule to the breaking of an arbitrary symmetry group, paying particular attention to the requirements of gauge invariance and current conservation.
Nucleon QCD sum rules in the instanton medium
Ryskin, M. G.; Drukarev, E. G. Sadovnikova, V. A.
2015-09-15
We try to find grounds for the standard nucleon QCD sum rules, based on a more detailed description of the QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rule equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small-size instantons contribution is w{sub s} ≈ 2/3.
New neutrino mass sum rule from the inverse seesaw mechanism
NASA Astrophysics Data System (ADS)
Dorame, L.; Morisi, S.; Peinado, E.; Valle, J. W. F.; Rojas, Alma D.
2012-09-01
A class of discrete flavor-symmetry-based models predicts constrained neutrino mass matrix schemes that lead to specific neutrino mass sum rules. One of these implies a lower bound on the effective neutrinoless double beta mass parameter, even for normal hierarchy neutrinos. Here we propose a new model based on the S4 flavor symmetry that leads to the new neutrino mass sum rule and discuss how to generate a nonzero value for the reactor angle θ13 indicated by recent experiments, and the resulting correlation with the solar angle θ12.
Decay Constants of Beauty Mesons from QCD Sum Rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2014-11-01
Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the M̅S̅ scheme m̅b(m̅b) ≈ 4:18 GeV; the sum-rule result fB ≈ 210-220 MeV for the B meson decay constant is substantially larger than the recent lattice-QCD finding fB ≈ 190 MeV: Requiring QCD sum rules to reproduce the lattice-QCD value of fB yields a significantly larger b-quark mass: m̅b(m̅b) = 4:247 GeV: (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants fD; fDs, fD* and fDs* are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants—and especially for the ratio fB* / fB—prove to be very sensitive to the specific scale setting.
Beauty vector meson decay constants from QCD sum rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2016-01-01
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Inequalities for frequency-moment sum rules of electron liquids
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1986-01-01
The relations between the various frequency-moment sum rules of electron liquids, which include even-power moments, are systematically examined by using the Cauchy-Schwarz and Hoelder inequalities. A relation involving the isothermal sound velocity and the kinetic and potential energies is obtained from one of the inequalities in the long-wavelength limit, and is generalized to arbitrary spatial dimensions.
Spectral sum rules for confining large-N theories
Cherman, Aleksey; McGady, David A.; Yamazaki, Masahito
2016-06-17
We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing ’t Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale Λ₋1. We find our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.
Optical conductivity and the sum rule in the DDW state
NASA Astrophysics Data System (ADS)
Aristov, D. N.; Zeyher, R.
2005-04-01
The density wave with d-wave order parameter (DDW) is possibly realized in the underdoped regime of high- Tc cuprates. The DDW state is characterized by two branches of low-lying electronic excitations, and the quantum mechanical current has in particular an inter-branch contribution. The latter component causes a finite-frequency response in the optical conductivity and a reduction of the Drude contribution. We show that this redistribution of the spectral weight leaves the optical sum mostly intact, so that the restricted optical sum rule is only weakly violated.
Strange quark condensate from QCD sum rules to five loops
NASA Astrophysics Data System (ADS)
Dominguez, Cesareo A.; Nasrallah, Nasrallah F.; Schilcher, Karl
2008-02-01
It is argued that it is valid to use QCD sum rules to determine the scalar and pseudoscalar two-point functions at zero momentum, which in turn determine the ratio of the strange to non-strange quark condensates Rsu = langlebar ssrangle/langlebar qqrangle with (q = u, d). This is done in the framework of a new set of QCD Finite Energy Sum Rules (FESR) that involve as integration kernel a second degree polynomial, tuned to reduce considerably the systematic uncertainties in the hadronic spectral functions. As a result, the parameters limiting the precision of this determination are ΛQCD, and to a major extent the strange quark mass. From the positivity of Rsu there follows an upper bound on the latter: \\overline{ms}(2 GeV) <= 121 (105) MeV, for ΛQCD = 330 (420) MeV.
Otto Stern, the Gdh Sum Rule and Various Spin Crises
NASA Astrophysics Data System (ADS)
Drechsel, D.
2001-02-01
The history of spin and anomalous magnetic moment is full of puzzles and "crises" from the first observations in the 1920's to the present day. The Gerasimov-Drell-Hearn sum rule connects the anomalous magnetic moment with the helicity dependent cross section for photoproduction, and as such checks the internal consistency of our understanding of the nucleon spin structure. Various generalizations of the sum rule have been proposed for the case of virtual photons, thus interpolating from the real photon point to deep inelastic scattering. A series of recent and newly proposed experiments with beam and target/recoil polarization will study this transition between the coherent spin-dependent response and the incoherent response of the partons in the scaling region.
Pseudoscalar glueball wave functions from QCD sum rules
Wakely, A.B.; Carlson, C.E. )
1992-01-01
Using QCD sum rules, we calculate the first few moments of the distribution amplitude of a pseudo- scalar glueball, in the approximation that the glueball is narrow. These moments then give the corresponding first few coefficients of the distribution amplitude for the glueball expanded in Gegenbauer polynomials. The distribution amplitude is rather close to its asymptotic form, and the glueball's decay constant'' is about 105 MeV for a pseudoscalar glueball mass of 2.0 GeV.
Heavy-meson decay constants from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2010-12-22
We sketch a recent sum-rule extraction of the decay constants of the heavy pseudoscalar mesons D, D{sub s}, B, and B{sub s} from the two-point correlator of heavy-light pseudoscalar currents. Our main emphasis lies on the control over all the uncertainties in the decay constants, related both to the input QCD parameters and to the limited accuracy of the method of sum rules. Gaining this control has become possible by application of our new procedure of extracting hadron observables based on a dual threshold depending on the Borel parameter. For the charmed-meson decay constants, we find fD = (206.2{+-}7.3{sub (OPE)}{+-}5.1{sub (syst)}) MeV, fD{sub s} = (245.3{+-}15.7{sub (OPE)}{+-}4.5{sub (syst)}) MeV. For the beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of the {ovr MS} mass of the b-quark, {bar m}{sub b}({bar m}{sub b}). By requiring our sum-rule estimate to match the average of the lattice determinations of f{sub B}, we extract the rather accurate value {bar m}{sub b}({bar m}{sub b}) = (4.245{+-}0.025) GeV. Feeding this parameter value into our sum-rule formalism leads to the beauty-meson decay constants fB = (193.4{+-}12.3{sub (OPE)}{+-}4.3{sub (syst)}) MeV, fB{sub s} = (232.5{+-}18.6{sub (OPE)}{+-}2.4{sub (syst)}) MeV.
On the loop approximation in nucleon QCD sum rules
Drukarev, E. G. Ryskin, M. G.; Sadovnikova, V. A.
2015-10-15
There was a general belief that the nucleon QCD sum rules which include only the quark loops and thus contain only the condensates of dimension d = 3 and d = 4 have only a trivial solution. We demonstrate that there is also a nontrivial solution. We show that it can be treated as the lowest order approximation to the solution which includes the higher terms of the Operator Product Expansion. Inclusion of the radiative corrections improves the convergence of the series.
Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule.
Cloët, Ian C; Bentz, Wolfgang; Thomas, Anthony W
2016-01-22
In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q|≳0.5 GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.
Sum rules for M2 and other cases
Kurath, D.
1995-08-01
Sum rules were derived for parity-changing operators consisting of an odd-l spherical harmonic coupled to the spin operator sigma. The conditions are that the valence nucleons are in the oscillator shell with Q quanta and the shell with Q-1 quanta is full and the shell with Q+1 quanta is empty. Thus this applies to the 1p, 2sd and 3pf as valence shells, where the sum rules would be useful for inelastic electron scattering and other reactions. In particular a complete M2 sum rule was derived including the weak contribution from the orbital operator. The contribution from the spurious center-of-mass motion was also derived. The expression was tested by comparing to summations of transition strengths given by shell-model calculations. For nuclei with mass greater than {approximately}A = 70 one would need to include the effect of the intruding level with Q+1 quanta and J = Q+3/2. This problem will be considered in the coming year.
Radiative corrections to the solar lepton mixing sum rule
NASA Astrophysics Data System (ADS)
Zhang, Jue; Zhou, Shun
2016-08-01
The simple correlation among three lepton flavor mixing angles ( θ 12, θ 13, θ 23) and the leptonic Dirac CP-violating phase δ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the solar lepton mixing sum rule θ 12 ≈ θ 12 ν + θ 13 cos δ, where θ 12 ν stems from a constant mixing pattern in the neutrino sector and takes the value of θ 12 ν = 45 ° for the bi-maximal mixing (BM), {θ}_{12}^{ν } = { tan}^{-1}(1/√{2}) ≈ 35.3° for the tri-bimaximal mixing (TBM) or {θ}_{12}^{ν } = { tan}^{-1}(1/√{5+1}) ≈ 31.7° for the golden-ratio mixing (GR), and investigate the renormalization-group (RG) running effects on lepton flavor mixing parameters when this sum rule is assumed at a superhigh-energy scale. For illustration, we work within the framework of the minimal supersymmetric standard model (MSSM), and implement the Bayesian approach to explore the posterior distribution of δ at the low-energy scale, which becomes quite broad when the RG running effects are significant. Moreover, we also discuss the compatibility of the above three mixing scenarios with current neutrino oscillation data, and observe that radiative corrections can increase such a compatibility for the BM scenario, resulting in a weaker preference for the TBM and GR ones.
Infrared modified QCD couplings and Bjorken sum rule
NASA Astrophysics Data System (ADS)
Khandramai, V. L.; Teryaev, O. V.; Gabdrakhmanov, I. R.
2016-02-01
We test the recently proposed “Massive” Perturbation Theory (MPT) for the description of the Γ1p-n data at low momentum transfers. The MPT constructed on the two grounds: the first is pQCD with only one parameter added, an effective “glueball mass” mp ≲ Mgl ≲ 1 GeV; serving as an infrared “regulator” the second stems out of the ghost- free Analytic Perturbation Theory comprising non-power perturbative expansion that makes it compatible with linear integral transformations. It is regular in the low-energy region and could serve as a practical means for the analysis of data below 1 GeV up to the IR-limit. We study the non-perturbative Bjorken sum rule higher twists correction by using the MPT, the integral representation for infinite sum of higher twists coefficients and the QCD-inspired model for the Q2-dependence of the generalized Gerasimov-Drell-Hearn sum rule.
Analysis of the scalar nonet mesons with QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2016-08-01
In this article, we assume that the nonet scalar mesons below 1 GeV are the two-quark-tetraquark mixed states and study their masses and pole residues using the QCD sum rules. In the calculation, we take into account the vacuum condensates up to dimension 10 and the O(α _s) corrections to the perturbative terms in the operator product expansion. We determine the mixing angles, which indicate the two-quark components are much larger than 50~%, then we obtain the masses and pole residues of the nonet scalar mesons.
3He Spin-Dependent Cross Sections and Sum Rules
Slifer, Karl; Amaryan, Moscov; Amaryan, Moskov; Auerbach, Leonard; Averett, Todd; Berthot, J.; Bertin, Pierre; Bertozzi, William; Black, Tim; Brash, Edward; Brown, D.; Burtin, Etienne; Calarco, John; Cates, Gordon; Chai, Zhengwei; Chen, Jian-Ping; Choi, Seonho; Chudakov, Eugene; Ciofi, Claudio; Cisbani, Evaristo; De Jager, Cornelis; Deur, Alexandre; DiSalvo, R.; Dieterich, Sonja; Djawotho, Pibero; Finn, John; Fissum, Kevin; Fonvieille, Helene; Frullani, Salvatore; Gao, Haiyan; Gao, Juncai; Garibaldi, Franco; Gasparian, Ashot; Gilad, Shalev; Gilman, Ronald; Glamazdin, Oleksandr; Glashausser, Charles; Glockle, W.; Golak, J.; Goldberg, Emma; Gomez, Javier; Gorbenko, Viktor; Hansen, Jens-Ole; Hersman, F.; Holmes, Richard; Huber, Garth; Hughes, Emlyn; Humensky, Thomas; Incerti, Sebastien; Iodice, Mauro; Jensen, S.; Jiang, Xiaodong; Jones, C.; Jones, G.; Jones, Mark; Jutier, Christophe; Kamada, H.; Ketikyan, Armen; Kominis, Ioannis; Korsch, Wolfgang; Kramer, Kevin; Kumar, Krishna; Kumbartzki, Gerfried; Kuss, Michael; Lakuriqi, Enkeleida; Laveissiere, Geraud; LeRose, John; Liang, Meihua; Liyanage, Nilanga; Lolos, George; Malov, Sergey; Marroncle, Jacques; McCormick, Kathy; McKeown, Robert; Meziani, Zein-Eddine; Michaels, Robert; Mitchell, Joseph; Nogga, Andreas; Pace, Emanuele; Papandreou, Zisis; Pavlin, Tina; Petratos, Gerassimos; Pripstein, David; Prout, David; Ransome, Ronald; Roblin, Yves; Rowntree, David; Rvachev, Marat; Sabatie, Franck; Saha, Arunava; Salme, Giovanni; SCOPETTA, S.; Skibinski, R.; Souder, Paul; Saito, Teijiro; Strauch, Steffen; Suleiman, Riad; Takahashi, Kazunori; Todor, Luminita; Tsubota, Hiroaki; Ueno, Hiroaki; Urciuoli, Guido; van der Meer, Rob; Vernin, Pascal; Voskanyan, Hakob; Witala, Henryk; Wojtsekhowski, Bogdan; Xiong, Feng; Xu, Wang; Yang, Jae-Choon; Zhang, Bin; Zolnierczuk, Piotr
2008-07-01
We present a measurement of the spin-dependent cross sections for the \\vec{^3He}(\\vec{e},e')X} reaction in the quasielastic and resonance regions at four-momentum transfer 0.1 < Q^2< 0.9 GeV^2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt--Cottingham and extended GDH sum rules for the first time. Impulse approximation and exact three-body Faddeev calculations are also compared to the data in the quasielastic region.
He3 Spin-Dependent Cross Sections and Sum Rules
NASA Astrophysics Data System (ADS)
Slifer, K.; Amarian, M.; Auerbach, L.; Averett, T.; Berthot, J.; Bertin, P.; Bertozzi, B.; Black, T.; Brash, E.; Brown, D.; Burtin, E.; Calarco, J.; Cates, G.; Chai, Z.; Chen, J.-P.; Choi, Seonho; Chudakov, E.; Ciofi Degli Atti, C.; Cisbani, E.; de Jager, C. W.; Deur, A.; Disalvo, R.; Dieterich, S.; Djawotho, P.; Finn, M.; Fissum, K.; Fonvieille, H.; Frullani, S.; Gao, H.; Gao, J.; Garibaldi, F.; Gasparian, A.; Gilad, S.; Gilman, R.; Glamazdin, A.; Glashausser, C.; Glöckle, W.; Golak, J.; Goldberg, E.; Gomez, J.; Gorbenko, V.; Hansen, J.-O.; Hersman, B.; Holmes, R.; Huber, G. M.; Hughes, E.; Humensky, B.; Incerti, S.; Iodice, M.; Jensen, S.; Jiang, X.; Jones, C.; Jones, G.; Jones, M.; Jutier, C.; Kamada, H.; Ketikyan, A.; Kominis, I.; Korsch, W.; Kramer, K.; Kumar, K.; Kumbartzki, G.; Kuss, M.; Lakuriqi, E.; Laveissiere, G.; Lerose, J. J.; Liang, M.; Liyanage, N.; Lolos, G.; Malov, S.; Marroncle, J.; McCormick, K.; McKeown, R. D.; Meziani, Z.-E.; Michaels, R.; Mitchell, J.; Nogga, A.; Pace, E.; Papandreou, Z.; Pavlin, T.; Petratos, G. G.; Pripstein, D.; Prout, D.; Ransome, R.; Roblin, Y.; Rowntree, D.; Rvachev, M.; Sabatié, F.; Saha, A.; Salmè, G.; Scopetta, S.; Skibiński, R.; Souder, P.; Saito, T.; Strauch, S.; Suleiman, R.; Takahashi, K.; Teijiro, S.; Todor, L.; Tsubota, H.; Ueno, H.; Urciuoli, G.; van der Meer, R.; Vernin, P.; Voskanian, H.; Witała, H.; Wojtsekhowski, B.; Xiong, F.; Xu, W.; Yang, J.-C.; Zhang, B.; Zolnierczuk, P.
2008-07-01
We present a measurement of the spin-dependent cross sections for the He→3(e→,e')X reaction in the quasielastic and resonance regions at a four-momentum transfer 0.1≤Q2≤0.9GeV2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt-Cottingham and extended Gerasimov-Drell-Hearn sum rules for the first time. The data are also compared to an impulse approximation calculation and an exact three-body Faddeev calculation in the quasielastic region.
Light-Cone Sum Rule Approach for Baryon Form Factors
NASA Astrophysics Data System (ADS)
Offen, Nils
2016-10-01
We present the state-of-the-art of the light-cone sum rule approach to Baryon form factors. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations.
Light-Cone Sum Rule Approach for Baryon Form Factors
NASA Astrophysics Data System (ADS)
Offen, Nils
2016-08-01
We present the state-of-the-art of the light-cone sum rule approach to Baryon form factors. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations.
Test of Sum Rules in Nucleon Transfer Reactions
NASA Astrophysics Data System (ADS)
Schiffer, J. P.; Hoffman, C. R.; Kay, B. P.; Clark, J. A.; Deibel, C. M.; Freeman, S. J.; Howard, A. M.; Mitchell, A. J.; Parker, P. D.; Sharp, D. K.; Thomas, J. S.
2012-01-01
The quantitative consistency of nucleon transfer reactions as a probe of the occupancy of valence orbits in nuclei is tested. Neutron-adding, neutron-removal, and proton-adding transfer reactions were measured on the four stable even Ni isotopes, with particular attention to the cross section determinations. The data were analyzed consistently in terms of the distorted wave Born approximation to yield spectroscopic factors. Valence-orbit occupancies were extracted, utilizing the Macfarlane-French sum rules. The deduced occupancies are consistent with the changing number of valence neutrons, as are the vacancies for protons, both at the level of <5%. While there has been some debate regarding the true “observability” of spectroscopic factors, the present results indicate that empirically they yield self-consistent results.
Isospin violation in QCD sum rules for baryons
Adami, C. ); Drukarev, E.G. ); Ioffe, B.L. )
1993-09-01
We thoroughly analyze isospin-violating effects in QCD sum rules for the masses of nucleons, [Sigma], and [Xi] hyperons. After comparing with experimental mass splittings in isotopic multiplets, we obtain for the isospin breaking in the quark condensate [l angle]0[vert bar][ital [bar u]u][minus][ital [bar d]d][vert bar]0[r angle]/[l angle]0[vert bar][ital [bar u]u][vert bar]0[r angle]=(2[plus minus]1)[times]10[sup [minus]3], a value significantly smaller than the one usually adopted. We present arguments in favor of our result and critically analyze previous estimates. The value of the quark mass difference [ital m][sub [ital d
Holographic RG flows, entanglement entropy and the sum rule
NASA Astrophysics Data System (ADS)
Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
2016-03-01
We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d = 2 and in d > 2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.
Sum Rules for Nucleon GPDs and Border Function Formulation
Radyushkin, Anatoly V.
2013-09-01
Recently developed new approach to model nucleon generalized parton distributions (GPDs) H and E is based on two types of their representation in terms of double distributions. Within this approach, we re-consider the derivation of GPD sum rules that allow to use border functions H(x,x) and E(x,x) instead of full GPDs H(x,\\xi) and E(x,\\xi) in the integrals producing Compton form factors of deeply virtual Compton scattering. Using factorized DD Ansatz to model GPDs, we discuss the relation between the border functions and underlying parton densities. We found that substantial contribution to H(x,x) border function comes from the extra term required by new DD representations and related to E(x,\\xi) GPD.
Spectral sum rules and search for periodicities in DNA sequences
NASA Astrophysics Data System (ADS)
Chechetkin, V. R.
2011-04-01
Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been strongly distorted by the random point mutations and insertions/deletions during molecular evolution. The latent periodicities in DNA sequences can be efficiently displayed by Fourier transform. The criteria of significance for observed periodicities are obtained via the comparison versus the counterpart characteristics of the reference random sequences. We show that the restrictions imposed on the significance criteria by the rigorous spectral sum rules can be rationally described with De Finetti distribution. This distribution provides the convenient intermediate asymptotic form between Rayleigh distribution and exact combinatoric theory.
Comparing T-odd and T-even spin sum rules
Teryaev, O.V.
2015-04-10
Sum rules for T-even and T-odd structure functions and parton distributions are considered. The case of spin-dependent distributions related to energy-momentum tensor (EMT) is specifically addressed. The Burkardt sum rule for T-odd Sivers functions may be related to EMT provided the imaginary prescription for gluonic pole correlator is incorporated. The momentum sum rule for deuteron tensor spin structure function allows one to probe indirectly the gravity couplings to quarks and gluons.
Symbolic methods for the evaluation of sum rules of Bessel functions
Babusci, D.; Dattoli, G.; Górska, K.; Penson, K. A.
2013-07-15
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics.
The leptonic Dirac CP-violating phase from sum rules
NASA Astrophysics Data System (ADS)
Girardi, I.; Petcov, S. T.; Titov, A. V.
2016-05-01
In the reference 3-neutrino mixing scheme with three light massive neutrinos, CP-violating effects in neutrino oscillations can be caused by the Dirac CP-violating phase δ present in the unitary neutrino mixing matrix U. Using the fact that U = U†eUv , where Ue and Uv are unitary matrices arising from the diagonalisation, respectively, of the charged lepton and neutrino mass matrices, we consider in a systematic way forms of Ue and Uv allowing us to express δ as a function of the neutrino mixing angles present in U and the angles contained in Uv. After obtaining sum rules for cos δ, we consider several forms of Uv dictated by, or associated with, symmetries, such as tri-bimaximal, bimaximal, etc., for which the angles in Uv are fixed. For each of these forms and forms of Ue allowing to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cos δ, using the prospective uncertainties in the determination of the mixing angles. Our results show that the measurement of δ along with improvement of the precision on the neutrino mixing angles can provide unique information about the possible existence of a new fundamental symmetry in the lepton sector.
Towards NNLO accuracy in the QCD sum rule for the kaon distribution amplitude
NASA Astrophysics Data System (ADS)
Chetyrkin, K. G.; Khodjamirian, A.; Pivovarov, A. A.
2008-03-01
We calculate the O (αs) and O (αs2) gluon radiative corrections to the QCD sum rule for the first Gegenbauer moment a1K of the kaon light-cone distribution amplitude. The NNLO accuracy is achieved for the perturbative term and quark-condensate contributions to the sum rule. A complete factorization is implemented, removing logarithms of s-quark mass from the coefficients in the operator-product expansion. The sum rule with radiative corrections yields a1K (1 GeV) = 0.10 ± 0.04.
Rate and CP-Asymmetry Sum Rules in B to K pi
Gronau, Michael; Rosner, Jonathan L.
2006-08-28
The observed violation of A{sub CP}(B{sup 0} {yields} K{sup +}{pi}{sup -}) = A{sub CP}(B{sup +} {yields} K{sup +}{pi}{sup 0}) has been recently mentioned as a puzzle for the standard model. They point out that while this violation may be accounted for by a large color-suppressed tree amplitude, a sum rule involving three or four B {yields} K{pi} CP asymmetries should hold. the current experimental status of these sum rules and of a sum rule for B {yields} K{pi} decay rates is presented.
A Precise Sum Rule among Four B -> K pi CP Asymmetries
Gronau, Michael; /SLAC /Technion
2005-08-29
A sum rule relation is proposed for direct CP asymmetries in B {yields} K{pi} decays. Leading terms are identical in the isospin symmetry limit, while subleading terms are equal in the flavor SU(3) and heavy quark limits. The sum rule predicts A{sub CP}(B{sup 0} {yields} K{sup 0}{pi}{sup 0}) = -0.17 {+-} 0.06 using current asymmetry measurements for the other three B {yields} K{pi} decays. A violation of the sum rule would be evidence for New Physics in b {yields} s{bar q}q transitions.
Spectral properties of mesons in hot and dense matter from energy weighted sum rules
Cabrera, D.; Polls, A.; Ramos, A.; Tolos, L.
2010-12-28
Energy weighted sum rules for the spectral function of mesons are derived, both in cold nuclear matter and at finite temperature, by matching the Dyson propagator with its spectral Lehmann representation at low and high energies. We illustrate our results by calculating the sum rules for specific models of the kaon and pion self-energy in a nuclear medium. We find satisfactory results from the lower energy weight sum rules, which reflect the contributions from the different quasi-particle and collective modes of the meson spectral function, and show examples of the sensitivity of the sum rules to model approximations. Finally, we discuss applications in asymmetric nuclear matter and in the study of the spectral properties of vector mesons.
Sum rules and static local-field corrections of electron liquids in two and three dimensions
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1984-01-01
The dielectric functions of electron liquids which take into account short-range electron-electron correlations via the static local-field corrections are examined in the light of the frequency-moment sum rules. The formation is given for degenerate as well as classical electron liquids in arbitrary (d) spatial dimensions, which is suitable for comparison between the two- and three-dimensional cases. By using the virial equations of state it is shown that such dielectric functions cannot satisfy the compressibility sum rule and the third-frequency-moment sum rule simultaneously. In the degenerate case, the plasmon, single-pair, and multipair contributions to the sum rules are analyzed, and the reason for this incompatibility is discussed.
Endpoint behavior of the pion distribution amplitude in QCD sum rules with nonlocal condensates
Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
2010-09-01
Starting from the QCD sum rules with nonlocal condensates for the pion distribution amplitude, we derive another sum rule for its derivative and its ''integral derivatives''--defined in this work. We use this new sum rule to analyze the fine details of the pion distribution amplitude in the endpoint region x{approx}0. The results for endpoint-suppressed and flattop (or flatlike) pion distribution amplitudes are compared with those we obtained with differential sum rules by employing two different models for the distribution of vacuum-quark virtualities. We determine the range of values of the derivatives of the pion distribution amplitude and show that endpoint-suppressed distribution amplitudes lie within this range, while those with endpoint enhancement--flat-type or Chernyak-Zhitnitsky like--yield values outside this range.
Structure-function sum rules for systems with large scattering lengths
NASA Astrophysics Data System (ADS)
Goldberger, Walter D.; Rothstein, Ira Z.
2012-01-01
We use a dispersion relation in conjunction with the operator product expansion (OPE) to derive model independent sum rules for the dynamic structure functions of systems with large scattering lengths. We present an explicit sum rule for the structure functions that control the density and spin response of the many-body ground state. Our methods are general and apply to either fermions or bosons which interact through two-body contact interactions with large scattering lengths. By employing a Borel transform of the OPE, the relevant integrals are weighted toward infrared frequencies, thus allowing for greater overlap low energy data. Similar sum rules can be derived for other response functions. The sum rules can be used to extract the contact parameter introduced by Tan, including universality violating corrections at finite scattering lengths.
Complex-energy approach to sum rules within nuclear density functional theory
NASA Astrophysics Data System (ADS)
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; Olsen, Erik
2015-04-01
Background: The linear response of the nucleus to an external field contains unique information about the effective interaction, the correlations governing the behavior of the many-body system, and the properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or the nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. Purpose: To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random-phase approximation (QRPA). Methods: To compute sum rules, we carry out contour integration of the response function in the complex-energy plane. We benchmark our results against the conventional matrix formulation of the QRPA theory, the Thouless theorem for the energy-weighted sum rule, and the dielectric theorem for the inverse-energy-weighted sum rule. Results: We derive the sum-rule expressions from the contour integration of the complex-energy FAM. We demonstrate that calculated sum-rule values agree with those obtained from the matrix formulation of the QRPA. We also discuss the applicability of both the Thouless theorem about the energy-weighted sum rule and the dielectric theorem for the inverse-energy-weighted sum rule to nuclear density functional theory in cases when the EDF is not based on a Hamiltonian. Conclusions: The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method
QCD Sum Rules for Magnetically Induced Mixing between ηc and J/ψ
Cho, Sungtae; Hattori, Koichi; Lee, Su Houng; Morita, Kenji; Ozaki, Sho
2014-10-20
We investigate the properties of charmonia in strong magnetic fields by using QCD sum rules. We show how to implement the mixing effects between ηc and J/ψ on the basis of field-theoretical approaches, and then show that the sum rules are saturated by the mixing effects with phenomenologically determined parameters. Consequently, we find that the mixing effects are the dominant contribution to the mass shifts of the static charmonia in strong magnetic fields.
Sum rules for magnetic moments and polarizabilities in QED and chiral effective-field theory
Barry Holstein; Vladimir Pascalutsa; Marc Vanderhaeghen
2005-08-01
We elaborate on a recently proposed extension of the Gerasimov-Drell-Hearn (GDH) sum rule which is achieved by taking derivatives with respect to the anomalous magnetic moment. The new sum rule features a linear relation between the anomalous magnetic moment and the dispersion integral over a cross-section quantity. We find some analogy of the linearized form of the GDH sum rule with the ''sideways dispersion relations''. As an example, we apply the linear sum rule to reproduce the famous Schwinger's correction to the magnetic moment in QED from a tree-level cross-section calculation and outline the procedure for computing the two-loop correction from a one-loop cross-section calculation. The polarizabilities of the electron in QED are considered as well by using the other forward-Compton-scattering sum rules. We also employ the sum rules to study the magnetic moment and polarizabilities of the nucleon in a relativistic chiral EFT framework. In particular we investigate the chiral extrapolation of these quantities.
Sum Rules of Charm C P Asymmetries beyond the SU(3 ) F Limit
NASA Astrophysics Data System (ADS)
Müller, Sarah; Nierste, Ulrich; Schacht, Stefan
2015-12-01
We find new sum rules between direct C P asymmetries in D meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies P and P A , which cannot be determined from branching ratios. In this way, we can make predictions about direct C P asymmetries in the standard model without ad hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3 ) F breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II, one will identify or constrain new-physics contributions to P or P A . The first sum rule correlates the C P asymmetries aCP dir in D0→K+K-, D0→π+π- , and D0→π0π0. We study the region of the aCP dir(D0→π+π-)-aCP dir(D0→π0π0) plane allowed by current data and find that our sum rule excludes more than half of the allowed region at 95% C.L. Our second sum rule correlates the direct C P asymmetries in D+→K¯0K+, Ds+→K0π+, and Ds+→K+π0.
Sum Rules of Charm CP Asymmetries beyond the SU(3)_{F} Limit.
Müller, Sarah; Nierste, Ulrich; Schacht, Stefan
2015-12-18
We find new sum rules between direct CP asymmetries in D meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies P and PA, which cannot be determined from branching ratios. In this way, we can make predictions about direct CP asymmetries in the standard model without ad hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3)_{F} breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II, one will identify or constrain new-physics contributions to P or PA. The first sum rule correlates the CP asymmetries a_{CP}^{dir} in D^{0}→K^{+}K^{-}, D^{0}→π^{+}π^{-}, and D^{0}→π^{0}π^{0}. We study the region of the a_{CP}^{dir}(D^{0}→π^{+}π^{-})-a_{CP}^{dir}(D^{0}→π^{0}π^{0}) plane allowed by current data and find that our sum rule excludes more than half of the allowed region at 95% C.L. Our second sum rule correlates the direct CP asymmetries in D^{+}→K[over ¯]^{0}K^{+}, D_{s}^{+}→K^{0}π^{+}, and D_{s}^{+}→K^{+}π^{0}. PMID:26722915
Sum Rules of Charm CP Asymmetries beyond the SU(3)_{F} Limit.
Müller, Sarah; Nierste, Ulrich; Schacht, Stefan
2015-12-18
We find new sum rules between direct CP asymmetries in D meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies P and PA, which cannot be determined from branching ratios. In this way, we can make predictions about direct CP asymmetries in the standard model without ad hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3)_{F} breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II, one will identify or constrain new-physics contributions to P or PA. The first sum rule correlates the CP asymmetries a_{CP}^{dir} in D^{0}→K^{+}K^{-}, D^{0}→π^{+}π^{-}, and D^{0}→π^{0}π^{0}. We study the region of the a_{CP}^{dir}(D^{0}→π^{+}π^{-})-a_{CP}^{dir}(D^{0}→π^{0}π^{0}) plane allowed by current data and find that our sum rule excludes more than half of the allowed region at 95% C.L. Our second sum rule correlates the direct CP asymmetries in D^{+}→K[over ¯]^{0}K^{+}, D_{s}^{+}→K^{0}π^{+}, and D_{s}^{+}→K^{+}π^{0}.
Is the Coulomb sum rule violated in nuclei?
NASA Astrophysics Data System (ADS)
Morgenstern, J.; Meziani, Z.-E.
2001-08-01
Guided by the experimental confirmation of the validity of the Effective Momentum Approximation (EMA) in quasi-elastic scattering off nuclei, we have re-examined the extraction of the longitudinal and transverse response functions in medium-weight and heavy nuclei. In the EMA we have performed a Rosenbluth separation of the available world data on 40Ca, 48Ca, 56Fe, 197Au, 208Pb and 238U. We find that the longitudinal response function for these nuclei is "quenched" and that the Coulomb sum is not saturated, at odds with claims in the literature.
Finite temperature effects and the validity of the Weinberg sum rules
NASA Astrophysics Data System (ADS)
Ayala, Alejandro; Dominguez, C. A.; Loewe, M.; Zhang, Y.
2016-05-01
Using resent independent results from QCD sum rules for the thermal evolution of hadronic parameters in the vector and the axial-vector channels, we discuss the saturation of the two Weinberg sum rules. It turn out that both sum rules are quite well satisfied in a wide range from T = 0 up to T/T c ≃ 0.7 — 0.8. At higher temperatures, coming closer to Tc , there is an asymmetry between both channels since in the vector case there is a leading order effect, proportional to T2 , due to a one loop pion contribution in the space-like region, which is absent in the axial-vector case. This leads then to a small deviation. More important, though, in this region the QCD sum rules for the hadronic parameters begin to have no solutions since the widths of the ρ and the a1-mesons diverge signaling the occurrence of deconfinement. Close to and at Tc there are no pions left in the medium and chiral symmetry is restored so that the Weinberg sum rules are trivially satisfied.
Constraints on Airy function zeros from quantum-mechanical sum rules
NASA Astrophysics Data System (ADS)
Belloni, M.; Robinett, R. W.
2009-02-01
We derive new constraints on the zeros of Airy functions by using the so-called quantum bouncer system to evaluate quantum-mechanical sum rules and perform perturbation theory calculations for the Stark effect. Using commutation and completeness relations, we show how to systematically evaluate sums of the form Sp(n) = ∑k≠n1/(ζk - ζn)p, for natural p > 1, where -ζn is the nth zero of Ai(ζ).
Nonperturbative explanation of the enhancement factors in the QCD sum rule for the {rho} meson
Nie, S.; Kuang, Y.; Wang, Q.; Yi, Y. |
1997-08-01
Taking the sum rule for the {rho} meson as an example, we study the possibility of explaining the phenomenological enhancement factors for certain terms in the vacuum expectation value of operator product expansion in the QCD sum rule. We take a QCD motivated extended Nambu{endash}Jona-Lasinio model as the low energy effective Lagrangian for QCD with which we calculate the nonperpturbative contributions to the vaccum condensate expansion to obtain the enhancement factors. Our result shows that such nonperturbative contributions can cause large enough enhancement factors which can be consistent with the phenomenological values. {copyright} {ital 1997} {ital The American Physical Society}
QCD sum rules for {rho} mesons in vacuum and in-medium, re-examined
Kwon, Youngshin; Weise, Wolfram; Procura, Massimiliano
2008-11-15
An updated investigation of QCD sum rules for the first two moments of {rho}-meson spectral functions, both in vacuum and in-medium, is performed with emphasis on the role of the scale related to spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral distributions do permit an accurate sum-rule analysis with controlled input including QCD condensates of the lowest dimensions, whereas higher moments are subject to uncertainties from higher dimensional condensates. Possible connections with Brown-Rho scaling are discussed. The factorization approximation for four-quark condensates is shown not to be applicable in any of the cases studied.
Pion-photon transition form factor in light-cone sum rules
Pimikov, A. V.; Bakulev, A. P.; Mikhailov, S. V.; Stefanis, N. G.
2012-10-23
We extract constraints on the pion distribution amplitude from available data on the pionphoton transition form factor in the framework of light-cone sum rules. A pronounced discrepancy (2.7 - 3){sigma} between the Gegenbauer expansion coefficients extracted from the CELLO, CLEO, and Belle experimental data relative to those from BaBar is found. Predictions for the pion-photon transition form factor are presented by employing a pion distribution amplitude obtained long ago from QCD sum rules with nonlocal condensates. These predictions comply with the Belle data but disagree with those of BaBar beyond 9 GeV{sup 2}.
Incomplete fusion studies near Coulomb barrier: a modified sum rule model
NASA Astrophysics Data System (ADS)
Bhujang, Bhushan; Das, Pragya; Singh, R. P.; Tripathi, R.; Tomar, B. S.
2013-03-01
The excitation functions of the evaporation residues, produced via complete fusion and incomplete fusion reactions of 11B + 122Sn, were measured for the projectile energy of around 6 MeV/A by the off-line gamma spectrometry. The cross sections have been compared with the statistical model code Projected Angular Momentum Coupled Evaporation (PACE4). The original sum rule model underestimated the ICF cross sections. We therefore made modification in the model mainly to incorporate the energy dependence in the definition of critical angular momentum. Using this modified sum rule model, we found a significant improvement in the results.
Conductivity sum rule, implication for in-plane dynamics, and c-axis response
NASA Astrophysics Data System (ADS)
Kim, Wonkee; Carbotte, J. P.
2000-10-01
Recently observed c-axis optical sum rule violations indicate non-Fermi-liquid in-plane behavior. For coherent c-axis coupling, the observed flat, nearly frequency-independent c-axis conductivity σ1(ω) implies a large in-plane scattering rate Γ around (0,π) and therefore any pseudogap that might form at low frequency in the normal state will be smeared. On the other hand, incoherent c-axis coupling places no restriction on the value of Γ and gives a more consistent picture of the observed sum-rule violation which, we find in some cases, can be less than half.
The Josephson effect and the requirements of causality II. The f-sum rule
NASA Astrophysics Data System (ADS)
Ferrell, Richard A.
1988-05-01
The Josepson effect is characterized by a frequency dependent conductance, σ(ω, φ). This describes the linear response of a junction biased at phase φ to a voltage signal oscillating at frequency ω. We find that the integrated value of the phase dependent part of Re σ(ω, φ) for frequencies greater than ω g, the gap frequency, is only 50% of that required by the f-sum rule. This violation of the sum rule suggests an unphysical feature of the standard tunneling Hamiltonian.
Complex-energy approach to sum rules within nuclear density functional theory
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; Olsen, Erik
2015-04-27
The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.
Complex-energy approach to sum rules within nuclear density functional theory
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; Olsen, Erik
2015-04-27
The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish anmore » efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.« less
Light-cone Sum Rules in Soft-Collinear Effective Theory
De Fazio, Fulvia; Feldmann, Thorsten; Hurth, Tobias; /CERN /SLAC
2005-06-20
We derive light-cone sum rules (LCSRs) for exclusive B-meson decays into light energetic hadrons from correlation functions within soft-collinear effective theory (SCET). In these sum rules the short-distance scale refers to ''hard-collinear'' interactions with virtualities of order {Lambda}{sub QCD}m{sub b}. Hard scales (related to virtualities of order m{sub b}{sup 2}) are integrated out and enter via external coefficient functions in the sum rule. Soft dynamics is encoded in light-cone distribution amplitudes for the B-meson, which describe both the factorizable and non-factorizable contributions to exclusive B-meson decay amplitudes. As an example, we provide a detailed study of the SCET sum rule for the B {yields} {pi} transition form factor at large recoil, including radiative corrections from hard-collinear loop diagrams at first order in the strong coupling constant. We find remarkable conceptual and numerical differences with the heavy-quark limit of the conventional LCSR approach in QCD.
Kramers-Kronig relations and sum rules for the second-harmonic susceptibility
NASA Astrophysics Data System (ADS)
Scandolo, S.; Bassani, F.
1995-03-01
A set of Kramers-Kronig relations are obtained for the second-harmonic generation susceptibility χ(2)(ω,ω). Together with the asymptotic behavior in the frequency variable they give a set of sum rules up to the fifth moment of the susceptibility.
Form factors and decay rate of Bc * Dsl+l- decays in the QCD sum rules
NASA Astrophysics Data System (ADS)
Zeynali, K.; Bashiry, V.; Zolfagharpour, F.
2014-08-01
Rare exclusive decays are analyzed in the framework of the three-point QCD sum rules approach. The two-gluon condensate corrections to the correlation function are included and the form factors of this transition are evaluated. Using the form factors, the decay width and integrated decay rate for these decays are also calculated.
Iso-vector form factors of the delta and nucleon in QCD sum rules
Ozpineci, A.
2012-10-23
Form factors are important non-perturbative properties of hadrons. They give information about the internal structure of the hadrons. In this work, iso-vector axial-vector and iso-vector tensor form factors of the nucleon and the iso-vector axial-vector {Delta}{yields}N transition form factor calculations in QCD Sum Rules are presented.
Energy-weighted sum rules connecting ΔZ = 2 nuclei within the SO(8) model
Štefánik, Dušan; Šimkovic, Fedor; Faessler, Amand
2013-12-30
Energy-weighted sum rules associated with ΔZ = 2 nuclei are obtained for the Fermi and the Gamow-Teller operators within the SO(8) model. It is found that there is a dominance of contribution of a single state of the intermediate nucleus to the sum rule. The results confirm founding obtained within the SO(5) model that the energy-weighted sum rules of ΔZ = 2 nuclei are governed by the residual interactions of nuclear Hamiltonian. A short discussion concerning some aspects of energy weighted sum rules in the case of realistic nuclei is included.
A QCD Sum Rule Approach with an Explicit Di-quark field
Kim, Kyung-il; Jido, Daisuke; Lee, Su Houng
2011-10-21
In hadron phenomenology, diquark structures can be an important degree of freedom in certain configurations. We investigate the possibility that the diquark structure can be treated as an elementary field in certain configurations. To start with, we assume that {Lambda} is composed of a spectator strange quark and a diquark. We construct a QCD sum rule for {Lambda}, where the input parameters are the diquark mass and its condensate, in addition to other parameters of QCD sum rules. We find good Borel curve for the {Lambda} mass for certain combinations of the diquark mass and condensate, and that smaller diquark condensate is needed when the diquark mass is increased to maintain the good Borel curve. The same sets of diquark mass and condensate are found to work well for {Lambda}{sub c} and {Lambda}{sub b}.
Pion-photon transition form factor in light-cone sum rules
NASA Astrophysics Data System (ADS)
Pimikov, A. V.; Bakulev, A. P.; Mikhailov, S. V.; Stefanis, N. G.
2012-10-01
We extract constraints on the pion distribution amplitude from available data on the pionphoton transition form factor in the framework of light-cone sum rules. A pronounced discrepancy (2.7 - 3)σ between the Gegenbauer expansion coefficients extracted from the CELLO, CLEO, and Belle experimental data relative to those from BaBar is found. Predictions for the pion-photon transition form factor are presented by employing a pion distribution amplitude obtained long ago from QCD sum rules with nonlocal condensates. These predictions comply with the Belle data but disagree with those of BaBar beyond 9 GeV2. This original article was incorrectly published with a corrupt version of Fig. 1. The corrigendum (which is attached to this article) includes the correct version of the figure.
Kramers-Kronig relations and sum rules in nonlinear optical spectroscopy.
Peiponen, Kai-Erik; Lucarini, Valerio; Saarinen, Jarkko J; Vartiainen, Erik
2004-05-01
The full potential of the Kramers-Kronig relations and sum rules for nonlinear susceptibilities has unfortunately drawn relatively little attention in nonlinear optical spectra analysis. In this feature article a simple treatment of an anharmonic oscillator model in description of the nonlinear susceptibility of media and holomorphic properties of the nonlinear susceptibility were utilized. Using such concepts, conventional Kramers-Kronig, multiply-subtractive Kramers-Kronig, and generalized Kramers-Kronig dispersion relations can be derived. We demonstrate how in practice the variety of different Kramers-Kronig relations mentioned above, as well as various sum rules, can be applied in nonlinear optical spectra analysis. As an example we treat the third-harmonic wave generation spectrum from a polymer.
Modification of Nucleon Spectral Function in Nuclear Matter from QCD Sum Rules
NASA Astrophysics Data System (ADS)
Ohtani, Keisuke; Gubler, Philipp; Oka, Makoto
In-medium spectral functions of the nucleon and its negative parity excited state in nuclear matter are investigated from QCD sum rules with the maximum entropy method (MEM). We construct the parity projected in-medium nucleon QCD sum rule with all known first-order αs corrections to the Wilson coefficients of the operator product expansion (OPE). It is found that the quark condensate < bar{q}q > and vector quark condensate < qdagger q > have dominant contributions and thus the in-medium behaviors of both positive and negative parity states are strongly affected by the density dependencies of these condensates. The density dependencies of the effective masses and vector self-energies are also examined.
Nucleon form factors to next-to-leading order with light-cone sum rules
Passek-Kumericki, K.; Peters, G.
2008-08-01
We have calculated the leading-twist next-to-leading order (NLO), i.e., O({alpha}{sub s}), correction to the light-cone sum rules prediction for the electromagnetic form factors of the nucleon. We have used the Ioffe nucleon interpolation current and worked in M{sub N}=0 approximation, with M{sub N} being the mass of the nucleon. In this approximation, only the Pauli form factor F{sub 2} receives a correction and the calculated correction is quite sizable (ca. 60%). The numerical results for the proton form factors show the improved agreement with the experimental data. We also discuss the problems encountered when going away from M{sub N}=0 approximation at NLO, as well as gauge invariance of the perturbative results. This work presents the first step towards the NLO accuracy in the light-cone sum rules for baryon form factors.
Coset construction and character sum rules for the doubly extended N = 4 superconformal algebras
NASA Astrophysics Data System (ADS)
Petersen, Jens Lyng; Taormina, Anne
1993-06-01
Character sum rules associated with the realization of the N = 4 superconformal algebra Ãγ on manifolds corresponding to the group cosets SU(3) k˜+ / U(1) are derived and developed as an important tool in obtaining the modular properties of Ãγ characters as well as information on certain extensions of that algebra. Their structure strongly suggests the existence of rational conformal field theories with central charges in the range 1 ⪕ c ⪕ 4. The corresponding characters appear in the massive sector of the sum rules and are completely specified in terms of the characters for the parafermionic theory SU(3)/(SU(2)×U(1)) and in terms of the branching functions of massless Ãγ characters into SU(2) k˜+× SU(2) 1 characters.
Sum rules for interaction of ϒ resonances with Zbπ
NASA Astrophysics Data System (ADS)
Voloshin, M. B.
2016-07-01
The strength of the amplitudes for the coupling between the bottomonium ϒ (n S ) states, the bottomonium-like isovector resonances Zb and a pion, ϒ (n S )Zbπ , is considered. These amplitudes describe the decays Zb→ϒ (n S )π for n =1 , 2, 3, and the processes ϒ (n S )→Zbπ for n =5 ,6 ,… with either Zb(10610 ) or Zb(10650 ). It is pointed out that analyticity and unitarity impose a sum rule for these couplings to each of the Zb resonances. With the currently available data it appears to be difficult or impossible to simultaneously satisfy the sum rules for the Zb(10610 ) and Zb(10650 ) resonances. This difficulty can be resolved if there is a considerable dissimilarity in the yield of the states Zb(10610 )π and Zb(10650 )π in the e+e- annihilation at energies above the ϒ (5 S ) resonance.
Collective excitations and sum rules for the Hubbard model in the spin-density-wave regime
NASA Astrophysics Data System (ADS)
Monien, H.; Bedell, K. S.
1992-02-01
A variational estimate for the spin-wave velocity of the one-band Hubbard model on a square lattice in the spin-density-wave regime is studied. The estimate is given by the ratio of the f-sum rule to the static structure factor of the transverse-spin response function. The known results for the Heisenberg model are used to obtain results for those quantities in the large-U limit of the Hubbard model. The f-sum rule and static structure factor are calculated using the random-phase approximation (RPA). The spin-wave velocity calculated in the RPA, in the spin-density wave ground state, violates the variational bound.
Sum-Rule Conserving Spectral Functions from the Numerical Renormalization Group
NASA Astrophysics Data System (ADS)
Weichselbaum, Andreas; von Delft, Jan
2007-08-01
We show how spectral functions for quantum impurity models can be calculated very accurately using a complete set of discarded numerical renormalization group eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our derivation avoids both the overcounting ambiguities and the single-shell approximation for the equilibrium density matrix prevalent in current methods, ensuring that relevant sum rules hold rigorously and spectral features at energies below the temperature can be described accurately.
Analysis of X(1576) as a Tetraquark State with the QCD Sum Rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang; Wan, Shao-Long
2006-12-01
We take the viewpoint that X(1576) is the tetraquark state which consists of a scalar diquark and an anti-scalar-diquark in relative P-wave, and calculate its mass in the framework of the QCD sum rule approach. The numerical value of the mass mX = (1.66±0.14) GeV is consistent with the experimental data. There might be some tetraquark components in the vector meson X(1576).
New identities from quantum-mechanical sum rules of parity-related potentials
NASA Astrophysics Data System (ADS)
Ayorinde, O. A.; Chisholm, K.; Belloni, M.; Robinett, R. W.
2010-06-01
We apply quantum-mechanical sum rules to pairs of one-dimensional systems defined by potential energy functions related by parity. Specifically, we consider symmetric potentials, V(x) = V(- x), and their parity-restricted partners, ones with V(x) but defined only on the positive half-line. We extend recent discussions of sum rules for the quantum bouncer by considering the parity-extended version of this problem, defined by the symmetric linear potential, V(z) = F|z| and find new classes of constraints on the zeros of the Airy function, Ai(ζ), and its derivative, Ai'(ζ). We also consider the parity-restricted version of the harmonic oscillator and find completely new classes of mathematical relations, unrelated to those of the ordinary oscillator problem. These two soluble quantum-mechanical systems defined by power-law potentials provide examples of how the form of the potential (both parity and continuity properties) affects the convergence of quantum-mechanical sum rules. We also discuss semi-classical predictions for expectation values and the Stark effect for these systems.
Ultrafast zero balance of the oscillator-strength sum rule in graphene
Kim, Jaeseok; Lim, Seong Chu; Chae, Seung Jin; Maeng, Inhee; Choi, Younghwan; Cha, Soonyoung; Lee, Young Hee; Choi, Hyunyong
2013-01-01
Oscillator-strength sum rule in light-induced transitions is one general form of quantum-mechanical identities. Although this sum rule is well established in equilibrium photo-physics, an experimental corroboration for the validation of the sum rule in a nonequilibrium regime has been a long-standing unexplored question. The simple band structure of graphene is an ideal system for investigating this question due to the linear Dirac-like energy dispersion. Here, we employed both ultrafast terahertz and optical spectroscopy to directly monitor the transient oscillator-strength balancing between quasi-free low-energy oscillators and high-energy Fermi-edge ones. Upon photo-excitation of hot Dirac fermions, we observed that the ultrafast depletion of high-energy oscillators precisely complements the increased terahertz absorption oscillators. Our results may provide an experimental priori to understand, for example, the intrinsic free-carrier dynamics to the high-energy photo-excitation, responsible for optoelectronic operation such as graphene-based phototransistor or solar-energy harvesting devices. PMID:24036567
Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma
NASA Astrophysics Data System (ADS)
Alastuey, Angel; Fantoni, Riccardo
2016-05-01
We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations. The induced particle densities, and the resulting induced charge density, are then computed within density functional theory, where the free energy is expanded in powers of the density gradients. The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations, which involves the isothermal compressibility as well as suitably defined partial compressibilities. The familiar Stillinger-Lovett condition is also recovered as a by-product of our method, suggesting that the fourth moment sum rule should hold in any conducting phase. This is explicitly checked in the low density regime, within the Abe-Meeron diagrammatical expansions. Beyond its own interest, the fourth-moment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical point.
Determining the Dirac CP violation phase in the neutrino mixing matrix from sum rules
NASA Astrophysics Data System (ADS)
Girardi, I.; Petcov, S. T.; Titov, A. V.
2015-05-01
Using the fact that the neutrino mixing matrix U = Ue† Uν, where Ue and Uν result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase δ present in U satisfies when Uν has a form dictated by, or associated with, discrete symmetries and Ue has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to Uν, so that reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge L‧ =Le -Lμ -Lτ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for δ in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for cos δ proposed in the literature, taking into account also the uncertainties in the measured values of sin2 θ12, sin2 θ23 and sin2 θ13. This allows us, in particular, to assess the accuracy of the predictions for cos δ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3σ experimentally allowed ranges.
Nature of the X(5568) — A critical Laplace sum rule analysis at N2LO
NASA Astrophysics Data System (ADS)
Albuquerque, R.; Narison, S.; Rabemananjara, A.; Rabetiarivony, D.
2016-06-01
We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)(bd¯) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (τ-sum rule variable, tc continuum threshold and subtraction constant μ). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results ⊕ the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173 ˜ 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavors (buds), do not support some previous interpretations of the D0 candidate,1 X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: sin 2𝜃 ≈ 0.15. One can also scan the region (2327 ˜ 2444) MeV (where the Ds0∗(2317) might be a good candidate) and the one (5173 ˜ 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or π+hadrons decays.
Nature of the X(5568) — A critical Laplace sum rule analysis at N2LO
NASA Astrophysics Data System (ADS)
Albuquerque, R.; Narison, S.; Rabemananjara, A.; Rabetiarivony, D.
2016-06-01
We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)(bd¯) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (τ-sum rule variable, tc continuum threshold and subtraction constant μ). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results ⊕ the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173 ˜ 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavors (buds), do not support some previous interpretations of the D0 candidate,1 X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: sin 2𝜃 ≈ 0.15. One can also scan the region (2327 ˜ 2444) MeV (where the Ds0∗(2317) might be a good candidate) and the one (5173 ˜ 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or π+hadrons decays.
Heavy-Quark Mass and Heavy-Meson Decay Constants from QCD Sum Rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2011-05-23
We present a sum-rule extraction of decay constants of heavy mesons from the two-point correlator of heavy-light pseudoscalar currents. Our primary concern is to control the uncertainties of the decay constants, induced by both input QCD parameters and limited accuracy of the sum-rule method. Gaining this control is possible by applying our novel procedure for the extraction of hadron observables utilizing Borel-parameter-depending dual thresholds. For the charmed mesons, we obtain f{sub D} (206.2{+-}7.3{sub (OPE){+-}}5.1{sub (syst)}) MeV and f{sub D{sub s}} (245.3{+-}15.7{sub (OPE){+-}}4.5{sub (syst)}) MeV. In the case of the beauty mesons, the decay constants prove to be extremely sensitive to the exact value of the b-quark MS mass m-bar{sub b}(m-bar{sub b}). By matching our sum-rule prediction for f{sub B} to the lattice outcomes, the very accurate b-mass value m-bar{sub b}(m-bar{sub b}) = (4.245{+-}0.025) GeV is found, which yields f{sub B} = (193.4{+-}12.3{sub (OPE){+-}}4.3{sub (syst)}) MeV and f{sub B{sub s}} (232.5{+-}18.6{sub (OPE){+-}}2.4{sub (syst)}) MeV.
Perturbative corrections to Λ b → Λ form factors from QCD light-cone sum rules
NASA Astrophysics Data System (ADS)
Wang, Yu-Ming; Shen, Yue-Long
2016-02-01
We compute radiative corrections to Λ b → Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ b -baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ b -baryon correlation function is justified at leading power in Λ /m b , with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to- B-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at {O}({α}_s) shift the Λ b → Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ b → Λ from factors we further investigate several decay observables in the electro-weak penguin Λ b → Λ ℓ + ℓ - transitions in the factorization limit (i.e., ignoring the "non-factorizable" hadronic effects which cannot be expressed in terms of the Λ b → Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.
QCD corrections to B → π form factors from light-cone sum rules
NASA Astrophysics Data System (ADS)
Wang, Yu-Ming; Shen, Yue-Long
2015-09-01
We compute perturbative corrections to B → π form factors from QCD light-cone sum rules with B-meson distribution amplitudes. Applying the method of regions we demonstrate factorization of the vacuum-to-B-meson correlation function defined with an interpolating current for pion, at one-loop level, explicitly in the heavy quark limit. The short-distance functions in the factorization formulae of the correlation function involves both hard and hard-collinear scales; and these functions can be further factorized into hard coefficients by integrating out the hard fluctuations and jet functions encoding the hard-collinear information. Resummation of large logarithms in the short-distance functions is then achieved via the standard renormalization-group approach. We further show that structures of the factorization formulae for fBπ+ (q2) and fBπ0 (q2) at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an exploratory phenomenological analysis of B → π form factors, paying attention to various sources of perturbative and systematic uncertainties, and extract |Vub | = (3.05-0.38+0.54|th. ± 0.09|exp.) ×10-3 with the inverse moment of the B-meson distribution amplitude ϕB+ (ω) determined by reproducing fBπ+ (q2 = 0) obtained from the light-cone sum rules with π distribution amplitudes. Furthermore, we present the invariant-mass distributions of the lepton pair for B → πℓνℓ (ℓ = μ, τ) in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the B → π form factors fBπ+ (q2) and fBπ0 (q2) in brief.
Relation between (e, e') sum rules in 6, 7Li and 4He nuclei: Experiment and cluster model
NASA Astrophysics Data System (ADS)
Efros, V. D.; Timchenko, I. S.; Buki, A. Yu.
2016-09-01
The sums over ( e, e') spectra of 6Li and 7Li nuclei which correspond to the longitudinal sum rule are studied. It is suggested that due to the cluster structure of the lithium isotopes these sums may approximately be expressed in terms of such a sum pertaining to the α-particle. Calculation of these sums is performed in the framework of cluster models with antisymmetrization done with respect to all the nucleons. At momentum transfers higher than 0.8 fm-1 the relations expressing the A = 6 or 7 sum in terms of the A = 4 sum prove to be valid with rather high accuracy. In the region of momentum transfers around 1 fm-1 the longitudinal correlation functions of 6Li and 7Li nuclei are found to be close to that of the α-particle. Basing on this, the difference between the q values at which the high- q limit of the inelastic sum rule is reached in the 6, 7Li cases and the 4He case is explained. The experimental longitudinal sums in the range between 0.450 and 1.625 fm-1 are employed to perform comparison with the theoretical sum rule calculated in the framework of cluster models. Out of the experimental sums, those in the range between 0.750 and 1.000 fm-1 in the 6Li case and between 0.750 and 1.125 fm-1 in the 7Li case are obtained in the present work. In the 6 Li case a complete agreement between experiment and the calculated sum rule is found while in the 7Li case an agreement only at a qualitative level is observed.
NASA Astrophysics Data System (ADS)
Huitu, Katri; Pandita, P. N.; Tiitola, Paavo
2015-10-01
We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which combines three supersymmetry breaking scenarios, namely anomaly mediation, gravity mediation and gauge mediation using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the supersymmetry breaking parameters in terms of the RGIs. We further discuss whether the supersymmetry breaking mediation mechanism can be determined using a limited set of invariants, and derive sum rules valid for DMMSB below the gauge messenger scale. In addition we examine the implications of the measured Higgs mass for the DMMSB spectrum.
In-Medium QCD Sum Rules for {rho}-Meson and Chiral Scale
Kwon, Youngshin; Weise, Wolfram
2011-10-21
In this talk, chiral scale, 4{pi}f{sub {pi}{approx}1} GeV, was introduced as an indicator of partial restoration of chiral symmetry at finite density or temperature, rather than the argument between mass shift and collisional broadening. We use the finite energy sum rules to determine the chiral scale identified with the separation scale of the low-energy resonance part from the high-energy continuum part of {rho}-meson spectral function. In this framework, in-medium {rho}-meson mass should be discussed in terms of the first two moments of the spectral function.
B ---> pi and B ---> K transitions from QCD sum rules on the light cone
Ball, P.
1998-09-01
I calculate the form factors describing semileptonic and penguin-induced decays of B mesons into light pseudoscalar mesons. The form factors are calculated from QCD sum rules on the light-cone including contributions up to twist 4, radiative corrections to the leading twist contribution and SU(3)-breaking effects. The theoretical uncertainty is estimated to be \\sim 15%. The heavy-quark-limit relations between semileptonic and penguin form factors are found to be valid in the full accessible range of momentum transfer.
{sup 3}He Spin-Dependent Cross Sections and Sum Rules
Slifer, K.; Auerbach, L.; Choi, Seonho; Incerti, S.; Lakuriqi, E.; Meziani, Z.-E.; Amarian, M.; Ketikyan, A.; Voskanian, H.; Averett, T.; Berthot, J.; Bertin, P.; DiSalvo, R.; Fonvieille, H.; Laveissiere, G.; Roblin, Y.
2008-07-11
We present a measurement of the spin-dependent cross sections for the {sup 3}He-vector (e-vector,e{sup '})X reaction in the quasielastic and resonance regions at a four-momentum transfer 0.1{<=}Q{sup 2}{<=}0.9 GeV{sup 2}. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt-Cottingham and extended Gerasimov-Drell-Hearn sum rules for the first time. The data are also compared to an impulse approximation calculation and an exact three-body Faddeev calculation in the quasielastic region.
NASA Astrophysics Data System (ADS)
Henderson, D.; Plischke, M.
1987-04-01
Starting from well-known relations for the derivatives of the radial distribution functions of a mixture of fluids, and allowing the diameter of one particle to become exceedingly large, three sum rules for a fluid with density inhomogeneities are obtained. None of these sum rules are new. However, the relation between the Lovett-Mou-Buff-Wertheim and the Born-Green hierarchy of equations seems not well known. The accuracy of a recent parametrization of the pair correlation of hard spheres near a hard wall and of the solutions of the Percus-Yevick and hypernetted-chain equation for this same function are examined by determination of how well these functions satisfy these sum rules and the accuracy of their surface tension, calculated from the sum rule of Triezenberg and Zwanzig. Generally speaking, the Percus-Yevick theory gives the best results and the hypernetted-chain approximation gives the worst results with the parametrization being intermediate.
NASA Technical Reports Server (NTRS)
Berk, A.; Temkin, A.
1985-01-01
A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.
Magnetic moment for the negative parity Λ → Σ0 transition in light cone QCD sum rules
NASA Astrophysics Data System (ADS)
Aliev, T. M.; Savcı, M.
2016-07-01
The magnetic moment of the Λ →Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
Ball, Patricia; Braun, Vladimir M.
1997-01-01
The existing calculations of the form factors describing the decay B→ρeν from QCD sum rules have yielded conflicting results at small values of the invariant mass squared of the lepton pair. We demonstrate that the disagreement originates from the failure of the short-distance expansion to describe the ρ meson distribution amplitude in the region where almost the whole momentum is carried by one of the constituents. This limits the applicability of QCD sum rules based on the short-distance expansion of a three-point correlation function to heavy-to-light transitions and calls for an expansion around the light cone, as realized in the light-cone sum rule approach. We derive and update light-cone sum rules for all the semileptonic form factors, using recent results on the ρ meson distribution amplitudes. The results are presented in detail together with a careful analysis of the uncertainties, including estimates of higher-twist effects, and compared to lattice calculations and recent CLEO measurements. We also derive a set of “improved” three-point sum rules, in which some of the problems of the short-distance expansion are avoided and whose results agree to good accuracy with those from light-cone sum rules.
Pion distribution amplitude extracted from the experimental data with the local duality sum rule
Guo Zekun; Liu Jueping
2008-10-01
The photon-to-pion transition form factor is investigated using the form of the renormalon-based twist-four pion distribution amplitude (DA) in the framework of the light-cone local-duality QCD sum rule, which, with suitable parameters, is insensitive to the higher-order Gegenbauer coefficients. With a careful determination for the insertion parameters so that the contribution from the higher-order Gegenbauer expansions is suppressed, the best-fit central values of the first two nontrivial Gegenbauer coefficients of the pion distribution amplitude are extracted out from the CLEO data to be a{sub 2}(1 GeV{sup 2})=0.145{+-}0.055 and a{sub 4}(1 GeV{sup 2})=-(0.125{+-}0.085), respectively. The rescaled photon-to-pion transition form factor with our best-fit parameters is consistent very well with both the CELLO data and the prediction of the interpolation formula in all the experimental accessible region of the momentum transfer. The shape of the pion distribution amplitude based on the two-parameter model favors the camel-like type, where the near-end-point values are suppressed more than the asymptotic DA, and satisfies the midpoint constraint from light-cone sum rules approximately.
Pion distribution amplitude extracted from the experimental data with the local duality sum rule
NASA Astrophysics Data System (ADS)
Guo, Ze-Kun; Liu, Jueping
2008-10-01
The photon-to-pion transition form factor is investigated using the form of the renormalon-based twist-four pion distribution amplitude (DA) in the framework of the light-cone local-duality QCD sum rule, which, with suitable parameters, is insensitive to the higher-order Gegenbauer coefficients. With a careful determination for the insertion parameters so that the contribution from the higher-order Gegenbauer expansions is suppressed, the best-fit central values of the first two nontrivial Gegenbauer coefficients of the pion distribution amplitude are extracted out from the CLEO data to be a2(1GeV2)=0.145±0.055 and a4(1GeV2)=-(0.125±0.085), respectively. The rescaled photon-to-pion transition form factor with our best-fit parameters is consistent very well with both the CELLO data and the prediction of the interpolation formula in all the experimental accessible region of the momentum transfer. The shape of the pion distribution amplitude based on the two-parameter model favors the camel-like type, where the near-end-point values are suppressed more than the asymptotic DA, and satisfies the midpoint constraint from light-cone sum rules approximately.
Light-cone sum rules for B → π form factors revisited
NASA Astrophysics Data System (ADS)
Duplancić, G.; Khodjamirian, A.; Mannel, Th.; Melić, B.; Offen, N.
2008-04-01
We reconsider and update the QCD light-cone sum rules for B → π form factors. The gluon radiative corrections to the twist-2 and twist-3 terms in the correlation functions are calculated. The overline-MS b-quark mass is employed, instead of the one-loop pole mass used in the previous analyses. The light-cone sum rule for f+Bπ(q2) is fitted to the measured q2-distribution in B → πlνl, fixing the input parameters with the largest uncertainty: the Gegenbauer moments of the pion distribution amplitude. For the B → π vector form factor at zero momentum transfer we predict f+Bπ(0) = 0.26+0.04-0.03. Combining it with the value of the product |Vubf+Bπ(0)| extracted from experiment, we obtain |Vub| = (3.5±0.4±0.2±0.1) × 10-3. In addition, the scalar and penguin B → π form factors f0Bπ(q2) and fTBπ(q2) are calculated.
Measurement of the Neutron Spin Structure Function and Its Implications for QCD Sum Rules
Xu, J
2004-01-06
The authors have determined the neutron spin structure function g{sub 1}{sup n} over the range 0.03 {le} x {le} 0.6 at an average Q{sup 2} of 2(GeV/c){sup 2} by measuring the asymmetry in deep inelastic scattering of polarized electrons from a polarized {sup 3}He target. The experiment was performed at SLAC and used energies between 19 and 26 GeV. The neutron asymmetry turned out to be small and negative, and the integral of the neutron spin structure function is {integral}{sub 0}{sup 1}g{sub 1}{sup n}(x)dx = -0.024 {+-} 0.006(stat.) {+-} 0.008(syst.). Combined with the current available worldwide proton data, this result confirmed the Bjorken sum rule at 10% level, once high-order perturbative QCD corrections are taken into account. The Ellis-Jaffe sum rule for the neutron predicts {integral}{sub 0}{sup 1} g{sub 1}{sup n}(x)dx = -0.010 {+-} 0.012, roughly consistent with their result.
Up- and down-quark masses from finite-energy QCD sum rules to five loops
Dominguez, C. A.; Nasrallah, N. F.; Roentsch, R. H.; Schilcher, K.
2009-01-01
The up- and down-quark masses are determined from an optimized QCD finite-energy sum rule involving the correlator of axial-vector divergences, to five-loop order in perturbative QCD, and including leading nonperturbative QCD and higher order quark-mass corrections. This finite-energy sum rule is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3-4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of contour improved perturbation theory, which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window s{sub 0}=1.0-4.0 GeV{sup 2}, where s{sub 0} is the radius of the integration contour in the complex energy (squared) plane. The results are m{sub u}(Q=2 GeV)=2.9{+-}0.2 MeV, m{sub d}(Q=2 GeV)=5.3{+-}0.4 MeV, and (m{sub u}+m{sub d})/2=4.1{+-}0.2 MeV (at a scale Q=2 GeV)
Up- and down-quark masses from finite-energy QCD sum rules to five loops
NASA Astrophysics Data System (ADS)
Dominguez, C. A.; Nasrallah, N. F.; Röntsch, R. H.; Schilcher, K.
2009-01-01
The up- and down-quark masses are determined from an optimized QCD finite-energy sum rule involving the correlator of axial-vector divergences, to five-loop order in perturbative QCD, and including leading nonperturbative QCD and higher order quark-mass corrections. This finite-energy sum rule is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3-4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of contour improved perturbation theory, which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window s0=1.0-4.0GeV2, where s0 is the radius of the integration contour in the complex energy (squared) plane. The results are mu(Q=2GeV)=2.9±0.2MeV, md(Q=2GeV)=5.3±0.4MeV, and (mu+md)/2=4.1±0.2MeV (at a scale Q=2GeV).
Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect
Golkar, Siavash; Nguyen, Dung X.; Son, Dam T.
2016-01-05
Here, we consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρT(ω) andmore » $$\\bar{p}$$T(ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q4 coefficient of the static structure factor S4, and the high-frequency shear modulus of the ground state μ∞, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S4 is bounded from below by |S–1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.« less
Viscosity of strongly interacting quantum fluids: Spectral functions and sum rules
Taylor, Edward; Randeria, Mohit
2010-05-15
The viscosity of strongly interacting systems is a topic of great interest in diverse fields. We focus here on the bulk and shear viscosities of nonrelativistic quantum fluids, with particular emphasis on strongly interacting ultracold Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral functions, {zeta}({omega}) and {eta}({omega}), respectively, to derive exact, nonperturbative results. Our results include a microscopic connection between the shear viscosity {eta} and the normal-fluid density {rho}{sub n}; sum rules for {zeta}({omega}) and {eta}({omega}) and their evolution through the BCS-BEC crossover (where BEC denotes Bose-Einstein condensate); and universal high-frequency tails for {eta}({omega}) and the dynamic structure factor S(q,{omega}). We use our sum rules to show that, at unitarity, {zeta}({omega}) is identically zero and thus relate {eta}({omega}) to density-density correlations. We predict that frequency-dependent shear viscosity {eta}({omega}) of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.
Finite amplitude method for discrete collective excited states and sum rules
NASA Astrophysics Data System (ADS)
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; Olsen, Erik
2014-09-01
The finite amplitude method (FAM) is one of the new efficient iterative methods for solving the QRPA problem, based on the linear response theory. The original FAM equations are solved with a small imaginary width introduced to the QRPA energy, and, up to present, its direct application to discrete excitations has not been fully accomplished. To this end we proposed a new formulation of the FAM using the contour integration technique. We show that the discrete QRPA amplitudes and energies can be expressed by means of contour integration around the QRPA poles in a complex-energy plane. We then discuss the contour integral formulation for the QRPA sum rules needed to constrain modern energy density functionals.
Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
NASA Astrophysics Data System (ADS)
Weichselbaum, Andreas; von Delft, Jan
2007-03-01
We show how spectral functions for quantum impurity models, i.e. nanosystem embedded in fermionic or bosonic environment, can be calculated very accurately using a complete set of ``discarded'' numerical renormalization group (NRG) eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our rigorous derivation avoids both the overcounting ambiguities and the single-shell approximation for the equilibrium density matrix prevalent in current methods including state of the art DM-NRG. The resulting procedure based on the full density matrix of the system (FDM-NRG) ensures that relevant sum rules hold rigorously and spectral features at energies below the temperature can be described accurately.
Sum rules and interlayer conductivity of high-T{sub c} cuprates.
Basov, D. N.; Woods, S. I.; Katz, A. S.; Singley, E. J.; Dynes, R. C.; Xu, M.; Hinks, D.; Homes, C. C.; Strongin, M.; Materials Science Division; Univ. of California at San Diego; Univ. of Chicago; BNL
1999-01-01
Analysis of the interlayer infrared conductivity of cuprate high-transition temperature superconductors reveals an anomalously large energy scale extending up to midinfrared frequencies that can be attributed to formation of the superconducting condensate. This unusual effect is observed in a variety of materials, including Tl{sub 2}Ba{sub 2}CuO{sub 6+x}, La{sub 2x}Sr{sub x}CuO{sub 4}, and YBa{sub 2}Cu{sub 3}O{sub 6.6}, which show an incoherent interlayer response in the normal state. Midinfrared range condensation was examined in the context of sum rules that can be formulated for the complex conductivity. One possible interpretation of these experiments is in terms of a kinetic energy change associated with the superconducting transition.
Malila, Jussi; McGraw, Robert; Laaksonen, Ari; Lehtinen, Kari E. J.
2015-01-07
Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give amore » general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.« less
Malila, Jussi; McGraw, Robert; Laaksonen, Ari; Lehtinen, Kari E. J.
2015-01-07
Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give a general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.
Mass tensor in the Bohr Hamiltonian from the nondiagonal energy weighted sum rules
Jolos, R. V.; Brentano, P. von
2009-04-15
Relations are derived in the framework of the Bohr Hamiltonian that express the matrix elements of the deformation-dependent components of the mass tensor through the experimental data on the energies and the E2 transitions relating the low-lying collective states. These relations extend the previously obtained results for the intrinsic mass coefficients of the well-deformed axially symmetric nuclei on nuclei of arbitrary shape. The expression for the mass tensor is suggested, which is sufficient to satisfy the existing experimental data on the energy weighted sum rules for the E2 transitions for the low-lying collective quadrupole excitations. The mass tensor is determined for {sup 106,108}Pd, {sup 108-112}Cd, {sup 134}Ba, {sup 150}Nd, {sup 150-154}Sm, {sup 154-160}Gd, {sup 164}Dy, {sup 172}Yb, {sup 178}Hf, {sup 188-192}Os, and {sup 194-196}Pt.
A predictive A model, charged lepton hierarchy and tri-bimaximal sum rule
NASA Astrophysics Data System (ADS)
Lin, Yin
2009-05-01
We propose a novel A model in which the Tri-Bimaximal (TB) neutrino mixing and the charged lepton mass hierarchy are reproduced simultaneously. At leading order, the residual symmetry of the neutrino sector is Z×Z which guarantees the TB mixing without adjusting ad hoc free parameters. In the charged lepton sector, one of the previous Z is maximally broken and the resulting mass matrix is nearly diagonal and hierarchical. A natural mechanism for the required vacuum alignment is given with the help of the supersymmetry and an Abelian symmetry factor. In our model, subleading effects which could lead to appreciable deviations from TB mixing are very restrictive giving rise to possible next-to-leading predictions. From an explicit example, we show that our "constrained" A model is a natural framework, based on symmetry principle, to incorporate the TB sum rule: sinθ=1/3+2√{2}(cosδsinθ)/3.
Study of the D*ρ system using QCD sum rules
Torres, A. Martínez; Khemchandani, K. P.; Nielsen, M.; Navarra, F. S.; Oset, E.
2014-11-11
In this proceeding we present a study of the D*ρ system made by using the method of QCD sum rules. Considering isospin and spin projectors, we investigate the different configurations and obtain three D* mesons with isospin I = 1/2, spin S = 0, 1, 2 and with masses 2500±67 MeV, 2523±60 MeV, and 2439±119 MeV, respectively. The last state can be related to D{sub 2}{sup *} (2460) (spin 2) listed by the Particle Data Group, while one of the first two might be associated with D*(2640), whose spin-parity is unknown. In the case of I = 3/2 we also find evidences of three states with spin 0, 1 and 2, respectively, with masses 2467±82 MeV, 2420±128 MeV, and 2550±56 MeV.
Pinched weights and duality violation in QCD sum rules: A critical analysis
Gonzalez-Alonso, Martin; Pich, Antonio; Prades, Joaquim
2010-07-01
We analyze the so-called pinched weights, that are generally thought to reduce the violation of quark-hadron duality in finite-energy sum rules. After showing how this is not true in general, we explain how to address this question for the left-right correlator and any particular pinched weight, taking advantage of our previous work [1], where the possible high-energy behavior of the left-right spectral function was studied. In particular, we show that the use of pinched weights allows to determine with high accuracy the dimension six and eight contributions in the operator-product expansion, O{sub 6}=(-4.3{sub -0.7}{sup +0.9})x10{sup -3} GeV{sup 6} and O{sub 8}=(-7.2{sub -5.3}{sup +4.2})x10{sup -3} GeV{sup 8}.
QCD sum rule calculation of quark-gluon three-body components in the B-meson wave function
NASA Astrophysics Data System (ADS)
Nishikawa, Tetsuo; Tanaka, Kazuhiro
2011-10-01
We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters λE and λH, which represent quark-gluon three-body components in the B-meson wave function. We update the sum rules for λE,H calculating the new higher-order contributions to the operator product expansion for the corresponding correlator, i.e., the order αs radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensate, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve stability of the corresponding Borel sum rules, modifying the values of λE,H.
QCD sum rule calculation of quark-gluon three-body components in the B-meson wave function
Nishikawa, Tetsuo; Tanaka, Kazuhiro
2011-10-21
We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters {lambda}{sub E} and {lambda}{sub H}, which represent quark-gluon three-body components in the B-meson wave function. We update the sum rules for {lambda}{sub E,H} calculating the new higher-order contributions to the operator product expansion for the corresponding correlator, i.e., the order {alpha}{sub s} radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensate, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve stability of the corresponding Borel sum rules, modifying the values of {lambda}{sub E,H}.
Yan, Xin -Hu; Ye, Yun -Xiu; Chen, Jian -Ping; Lu, Hai -Jiang; Zhu, Peng -Jia; Jiang, Feng -Jian
2015-07-17
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at Jefferson Lab. Radiation and ionization energy loss are discussed for $^{12}C$ elastic scattering simulation. The relative momentum ratio $\\frac{\\Delta p}{p}$ and $^{12}C$ elastic cross section are compared without and with radiation energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for $^{12}C$ elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment.
Yan, Xin -Hu; Ye, Yun -Xiu; Chen, Jian -Ping; Lu, Hai -Jiang; Zhu, Peng -Jia; Jiang, Feng -Jian
2015-07-17
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at Jefferson Lab. Radiation and ionization energy loss are discussed formore » $$^{12}C$$ elastic scattering simulation. The relative momentum ratio $$\\frac{\\Delta p}{p}$$ and $$^{12}C$$ elastic cross section are compared without and with radiation energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for $$^{12}C$$ elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment.« less
Sum rules and properties in time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Qian, Zhixin; Sahni, Viraht
2001-04-01
Time-dependent quantal density-functional theory (Q-DFT) is a description of the s-system of noninteracting fermions with electronic density equivalent to that of Schrödinger theory, in terms of fields whose sources are quantum-mechanical expectations of Hermitian operators. The theory delineates and defines the contribution of each type of electron correlation to the local electron-interaction potential νee(r,t) of the s system. These correlations are due to the Pauli exclusion principle, Coulomb repulsion, correlation-kinetic, and correlation-current-density effects, the latter two resulting, respectively, from the difference in kinetic energy and current density between the interacting Schrödinger and noninteracting systems. We employ Q-DFT to prove the following sum rules and properties of the s system: (i) the components of the potential due to these correlations separately exert no net force on the system; (ii) the torque of the potential is finite and due solely to correlation-current-density effects; (iii) two sum rules involving the curl of the dynamic electron-interaction kernel defined as the functional derivative of νee(r,t) are derived and shown to depend on the frequency dependent correlation-current-density effect. Furthermore, via adiabatic coupling constant (λ) perturbation theory, we prove: (iv) the exchange potential νx(r,t) is the work done in a conservative field representative of Pauli correlations and lowest-order O(λ) correlation-kinetic and correlation-current-density effects; (v) the correlation potential νc(r,t) commences in O(λ2), and, at each order, it is the work done in a conservative field representative of Coulomb correlations and correlation-kinetic and correlation-current-density effects; (vi) we derive the integral virial theorem relating νee(r,t) to the electron-interaction and correlation-kinetic energy for arbitrary coupling constant strength λ, and show there are no explicit correlation
Sum Rule Constraints and the Quality of Approximate Kubo-Transformed Correlation Functions.
Hernández de la Peña, Lisandro
2016-02-11
In this work, a general protocol for evaluating the quality of approximate Kubo correlation functions of nontrivial systems in many dimensions is discussed. We first note that the generalized deconvolution of the Kubo transformed correlation function onto a time correlation function at a given value τ in imaginary time, such that 0 < τ < βℏ, leads to a series of sum rules applicable to the nth derivative of the Kubo function and whose iterative extension allows us to link derivatives of different order in the corresponding correlation functions. We focus on the case when τ = βℏ/2, for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibits a polynomial divergence. It is then shown that thermally symmetrized static averages, and the averages of the corresponding time derivatives, are ideally suited to investigate the quality of approximate Kubo correlation functions at successively larger (and up to arbitrarily long) times. This overall strategy is illustrated analytically for a harmonic system and numerically for a multidimensional double-well potential and a Lennard-Jones fluid. The analysis includes an assessment of RPMD position autocorrelation results as a function of the number of dimensions in a double-well potential and of the RPMD velocity autocorrelation function of liquid neon at 30 K.
Sum Rule Constraints and the Quality of Approximate Kubo-Transformed Correlation Functions.
Hernández de la Peña, Lisandro
2016-02-11
In this work, a general protocol for evaluating the quality of approximate Kubo correlation functions of nontrivial systems in many dimensions is discussed. We first note that the generalized deconvolution of the Kubo transformed correlation function onto a time correlation function at a given value τ in imaginary time, such that 0 < τ < βℏ, leads to a series of sum rules applicable to the nth derivative of the Kubo function and whose iterative extension allows us to link derivatives of different order in the corresponding correlation functions. We focus on the case when τ = βℏ/2, for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibits a polynomial divergence. It is then shown that thermally symmetrized static averages, and the averages of the corresponding time derivatives, are ideally suited to investigate the quality of approximate Kubo correlation functions at successively larger (and up to arbitrarily long) times. This overall strategy is illustrated analytically for a harmonic system and numerically for a multidimensional double-well potential and a Lennard-Jones fluid. The analysis includes an assessment of RPMD position autocorrelation results as a function of the number of dimensions in a double-well potential and of the RPMD velocity autocorrelation function of liquid neon at 30 K. PMID:26786406
Extremely Correlated Fermi Liquid theory: Imposing the hole density sum-rule
NASA Astrophysics Data System (ADS)
Shastry, B. Sriram
The analytical theory of extremely strongly correlated Fermi liquids (ECFL) for the large U models, when applied to Cuprate superconductors in the nodal direction, provides ARPES spectral line shapes that are very close to experiments. Approximate lowest order calculations within this formalism also closely reproduce the spectral line shapes for the single impurity Anderson model found using the Numerical Renormalization Group. Similarly excellent comparison is possible with the Dynamical Mean Field Theory self energy for the Hubbard model in high dimensions. However these calculations yields too large an energy scale for frequency dependence, in the proximity of integer (or Mott) filling. We show that the theory permits the imposition of sum rules for hole density, rather than the electron density used earlier, on the Greens functions of the theory. The numerical results of these variants are presented, and compared to the earlier calculations. The new results go a long way towards resolving the energy scale problem, while retaining the excellence of line shapes. The work at UCSC was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award # FG02-06ER46319.
NASA Astrophysics Data System (ADS)
Rice, T. M.
2006-02-01
The Luttinger sum rule is usually considered for Landau Fermi liquids in which the single particle Green's function G(k, 0) changes sign at the the Fermi surface by passing through infinity. However the general proof allows also for a sign change at which G has a zero. A recent analysis by Konik and coworkers considers a model of 2-leg Hubbard ladders weakly coupled by a small long range interladder tunneling. At half-filling a semimetallic state with small Fermi pockets is induced beyond a threshold tunneling strength. The sign changes in G(k, 0) relevent for the Luttinger sum rule now take place at surfaces with both zeros and infinities. The zero surfaces differ from the minimum gap surfaces. The latter are often used in ARPES experiments on underdoped cuprates to obtain an underlying Fermi surface but this procedure leads to problems with the Luttinger sum rule. Some speculations on how the Luttinger sum rule should be applied to the pseudogap phase of the underdoped cuprates are included.
Twist-3 distribution amplitudes of scalar mesons from QCD sum rules
Lue Caidian; Wang Yuming; Zou Hao
2007-03-01
We study the twist-3 distribution amplitudes for scalar mesons made up of two valence quarks based on QCD sum rules. By choosing the proper correlation functions, we derive the moments of the scalar mesons up to the first two orders. Making use of these moments, we then calculate the first two Gegenbauer coefficients for twist-3 distribution amplitudes of scalar mesons. It is found that the second Gegenbauer coefficients of scalar density twist-3 distribution amplitudes for K{sub 0}* and f{sub 0} mesons are quite close to that for a{sub 0}, which indicates that the SU(3) symmetry breaking effect is tiny here. However, this effect could not be neglected for the forth Gegenbauer coefficients of scalar twist-3 distribution amplitudes between a{sub 0} and f{sub 0}. Besides, we also observe that the first two Gegenbauer coefficients corresponding to the tensor current twist-3 distribution amplitudes for all the a{sub 0}, K{sub 0}* and f{sub 0} are very small. The renormalization group evolution of condensates, quark masses, decay constants and moments are considered in our calculations. As a by-product, it is found that the masses for isospin I=1 (1/2) scalar mesons are around 1.27{approx}1.41 GeV and 1.44{approx}1.56 GeV respectively, while the mass for isospin state composed of ss is 1.62{approx}1.73 GeV.
B → Vℓ+ℓ- in the Standard Model from light-cone sum rules
NASA Astrophysics Data System (ADS)
Bharucha, Aoife; Straub, David M.; Zwicky, Roman
2016-08-01
We present B q → ρ, B q → ω, B q → K ∗, B s → K ∗ and B s → ϕ form factors from light-cone sum rules (LCSR) at {O}({α}_s) for twist-2 and 3 and {O}({α}_s^0) for twist-4 with updated hadronic input parameters. Three asymptotic light-cone distribution amplitudes of twist-4 (and 5) are determined, necessary for the form factors to obey the equations of motion. It is argued that the latter constrain the uncertainty of tensor-to-vector form factor ratios thereby improving the prediction of zeros of helicity amplitudes of major importance for B → K ∗ℓℓ angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low q 2 as well as combined fits to LCSR and lattice results covering the entire kinematic range for B q → K ∗, B s → K ∗ and B s → ϕ. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for B → K ∗γ as well as B → K ∗ℓ+ℓ- and B s → ϕμ + μ - at low dilepton invariant mass. Employing our B → ( ρ,ω) form factor results we extract the CKM element | V ub| from the semileptonic decays B → ( ρ, ω)ℓ ν and find good agreement with other exclusive determinations.
NASA Astrophysics Data System (ADS)
Yan, Xin-Hu; Ye, Yun-Xiu; Chen, Jian-Ping; Lu, Hai-Jiang; Zhu, Peng-Jia; Jiang, Feng-Jian
2015-07-01
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at the Jefferson Lab. Radiation and ionization energy loss are discussed for 12C elastic scattering simulation. The relative momentum ratio \\frac{{Δ p}}{p} and 12C elastic cross section are compared without and with radiative energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for 12C elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment. Supported by National Natural Science Foundation of China (11135002, 11275083), US Department of Energy contract DE-AC05-84ER-40150 under which Jefferson Science Associates operates the Thomas Jefferson National Accelerator Facility and Natural Science Foundation of An'hui Educational Committee (KJ2012B179)
K 0- overlineK0 mixing and the CKM parameters (ϱ, η) from the Laplace sum rules
NASA Astrophysics Data System (ADS)
Narison, S.
1995-02-01
Using the Laplace sum rule (LSR) approach, which is less affected by the contribution of the higher mass hadronic states than the Finite Energy Sum Rule (FESR), we test the reliability of the existing estimate of the K 0- overlineK0 mixing parameter from the four-quark two-point correlator. We obtain, for the renormalization group invariant B-parameter [ {f K}/{(1.2f π) }] 2B̂K, the upper bound: 0.83 and the conservative estimate: 0.58 ± 0.22 from the LSR method. Combining the previous estimate with the updated value of f BB B=(1.49±0.14)f π obtained from the same LSR method, one can deduce the fitted values ( ϱ, η) f (0.09, 0.41) of the CKM parameters.
Unitarity sum rules, three-site moose model, and the ATLAS 2 TeV diboson anomalies
NASA Astrophysics Data System (ADS)
Abe, Tomohiro; Nagai, Ryo; Okawa, Shohei; Tanabashi, Masaharu
2015-09-01
We investigate W' interpretations for the ATLAS 2 TeV diboson anomalies. The roles of the unitarity sum rules, which ensure the perturbativity of the longitudinal vector boson scattering amplitudes, are emphasized. We find the unitarity sum rules and the custodial symmetry are powerful enough to predict various nontrivial relations among W W Z', W Z W', W W h , W W'h and Z Z'h coupling strengths in a model independent manner. We also perform surveys in the general parameter space of W' models and find the ATLAS 2 TeV diboson anomalies may be interpreted as a W' particle of the three-site moose model, i.e., a Kaluza-Klein like particle in a deconstructed extra dimension model. It is also shown that the nonstandard-model-like Higgs boson is favored by the present data to interpret the ATLAS diboson anomalies as the consequences of the W' and Z' bosons.
A QCD sum rule calculation of the X± (5568) → Bs0 π± decay width
NASA Astrophysics Data System (ADS)
Dias, J. M.; Khemchandani, K. P.; Martínez Torres, A.; Nielsen, M.; Zanetti, C. M.
2016-07-01
To understand the nature of the X (5568), recently observed in the mass spectrum of the Bs0 π± system by the D0 Collaboration, we have investigated, in a previous work, a scalar tetraquark (diquak-antidiquark) structure for it, within the two-point QCD sum rules method. We found that it is possible to obtain a stable value of the mass compatible with the D0 result, although a rigorous QCD sum rule constrained analysis led to a higher value of mass. As a continuation of our investigation, we calculate the width of the tetraquark state with same quark content as X (5568), to the channel Bs0 π±, using the three-point QCD sum rule. We obtain a value of (20.4 ± 8.7) MeV for the mass ∼ 5568 MeV, which is compatible with the experimental value of 21.9 ± 6.4 (sta)-2.5+5.0 (syst) MeV /c2. We find that the decay width to Bs0 π± does not alter much for a higher mass state.
B{sub (s)}{yields}S transitions in the light cone sum rules with the chiral current
Sun Yanjun; Li Zuohong; Huang Tao
2011-01-15
We make a QCD light-cone sum rule assessment of B{sub (s)} semileptonic decays to a light scalar meson, B{sub (s)}{yields}Sl{nu}{sub l}, Sll(l=e,{mu},{tau}). Chiral current correlators are used and calculations are performed at leading order in {alpha}{sub s}. Having little knowledge of the ingredients of the scalar mesons, we confine ourself to the two-quark picture for them and work with the two possible scenarios. The resulting sum rules for the form factors receive no contributions from the twist-3 distribution amplitudes, in comparison with the calculation of the conventional light-cone sum rule approach where the twist-3 parts usually play an important role. We specify the range of the squared momentum transfer q{sup 2}, in which the operator product expansion for the correlators remains valid approximately. It is found that the form factors satisfy a relation consistent with the prediction of soft collinear effective theory. In the effective range we investigate behaviors of the form factors and differential decay widths and compare our calculations with the observations from other approaches.
NASA Astrophysics Data System (ADS)
Delion, Doru S.; Schuck, Peter; Tohyama, Mitsuru
2016-02-01
The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuously broken symmetry, this being the main focus of the present article. Correlations beyond standard RPA are summed up correcting for the quasi-boson approximation in standard RPA. Desirable properties of standard RPA such as fulfillment of energy weighted sum rule and appearance of Goldstone (zero) modes are kept. We show theoretically and, for a model case, numerically that, indeed, SCRPA maintains all properties of standard RPA for practically all situations of spontaneously broken symmetries. A simpler approximate form of SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equations are first outlined as an eigenvalue problem, but it is also shown how an equivalent many body Green's function approach can be formulated.
Babusci, D.; Giordano, G.; Baghaei, H.; Cichocki, A.; Blecher, M.; Breuer, M.; Commeaux, C.; Didelez, J.P.; Caracappa, A.; Fan, Q.
1995-12-31
Energy weighted integrals of the difference in helicity-dependent photo-production cross sections ({sigma}{sub {1/2}} - {sigma}{sub 3/2}) provide information on the nucleon`s Spin-dependent Polarizability ({gamma}), and on the spin-dependent part of the asymptotic forward Compton amplitude through the Drell-Hearn-Gerasimov (DHG) sum rule. (The latter forms the Q{sup 2}=0 limit of recent spin-asymmetry experiments in deep-inelastic lepton-scattering.) There are no direct measurements of {sigma}{sub {1/2}} or {sigma}{sub 3/2}, for either the proton or the neutron. Estimates from current {pi}-photo-production multipole analyses, particularly for the proton-neutron difference, are in good agreement with relativistic-l-loop Chiral calculations ({chi}PT) for {gamma} but predict large deviations from the DHG sum rule. Either (a) both the 2-loop corrections to the Spin-Polarizability are large and the existing multipoles are wrong, or (b) modifications to the Drell-Hearn-Gerasimov sum rule are required to fully describe the isospin structure of the nucleon. The helicity-dependent photo-reaction amplitudes, for both the proton and the neutron, will be measured at LEGS from pion-threshold to 470 MeV. In these double-polarization experiments, circularly polarized photons from LEGS will be used with SPHICE, a new frozen-spin target consisting of {rvec H} {center_dot} {rvec D} in the solid phase. Reaction channels will be identified in SASY, a large detector array covering about 80% of 4{pi}. A high degree of symmetry in both target and detector will be used to minimize systematic uncertainties.
NASA Astrophysics Data System (ADS)
Ikawa, Shun-ichi; Yamazaki, Shuichi; Kimura, Masao
1981-06-01
Another form of the sum rule for dipolar absorptions has been derived by means of quantum statistics. The difference between this and usually used form results from a quantum effect on the molecular rotational motion. By the joint use of the two forms, average rotational kinetic energies of water molec in the liquid and solid phases and some dipolar molecules in solutions have been estimated. It has been shown that the average rotational kinetic energ larger than the value expected from the classical equipartition rule, with an increase in the hindering potential for the rotational motion of the mole The dipole moments of water molecules in liquid and solid water have been estimated. These are considerably smaller than the gas-phase value.
Energy-weighted sum rules and the analysis of vibrational structure in molecular spectra
NASA Astrophysics Data System (ADS)
Smith, W. L.
2015-10-01
The energy-weighted sum SV = Σn (E‧n - E″m)|<ψ″m|ψ‧n>|2 = <ψ″m|ΔV|ψ″m> for the vibrational potential functions V‧, V″ associated with transitions between two electronic states of diatomic molecular species is investigated and specific formulae are given using Morse functions for V‧ and V″. It is found that these formulae are useful approximations which provide a convenient way to analyse the vibrational structure of real spectra to give estimates of molecular parameters such as the change in internuclear distance accompanying a transition.
NASA Astrophysics Data System (ADS)
Wu, Xing-Gang
2008-10-01
We present an improved analysis of the constraints on the first two Gegenbauer moments, a {2/ π } and a {4/ π }, of the pion’s leading-twist distribution amplitude from a QCD light-cone sum rule analysis of the B→ π weak transition form factor f +( q 2). A proper chiral current is adopted in QCD light-cone sum rules so as to eliminate the most uncertain twist-3 contributions to f +( q 2), and then we concentrate our attention on the properties of the leading-twist pionic DA. A nearly model-independent f +( q 2), based on the spectrum of B→ π l ν decays from BaBar, together with uncertainties, is adopted as the standard shape for f +( q 2) for our discussion. From a minimum χ 2-fit and by taking the theoretical uncertainties into account, we obtain a {2/ π }(1 GeV)=0.17{-0.17/+0.15} and a {4/ π }(1 GeV)=-0.06{-0.22/+0.20} at the 1 σ confidence level for m {b/*}∈[4.7,4,8] GeV.
OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2011-01-01
We present a sum-rule extraction of the decay constants of the charmed mesons D and Ds from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running MS¯ masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the MS¯ mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the MS¯-mass correlator. Second, making use of the OPE in terms of the MS¯ mass, we determine the decay constants of both D and Ds mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules. PMID:21949465
OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules.
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2011-06-27
We present a sum-rule extraction of the decay constants of the charmed mesons D and Ds from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running MS¯ masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the MS¯ mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the MS¯-mass correlator. Second, making use of the OPE in terms of the MS¯ mass, we determine the decay constants of both D and Ds mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules.
The spin structure function g1p of the proton and a test of the Bjorken sum rule
NASA Astrophysics Data System (ADS)
Adolph, C.; Akhunzyanov, R.; Alexeev, M. G.; Alexeev, G. D.; Amoroso, A.; Andrieux, V.; Anosov, V.; Austregesilo, A.; Azevedo, C.; Badełek, B.; Balestra, F.; Barth, J.; Baum, G.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E. R.; Birsa, R.; Bisplinghoff, J.; Bodlak, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Büchele, M.; Burtin, E.; Capozza, L.; Chang, W.-C.; Chiosso, M.; Choi, I.; Chung, S. U.; Cicuttin, A.; Crespo, M. L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S. S.; Dasgupta, S.; Denisov, O. Yu.; Dhara, L.; Donskov, S. V.; Doshita, N.; Duic, V.; Dziewiecki, M.; Efremov, A.; Eversheim, P. D.; Eyrich, W.; Ferrero, A.; Finger, M.; Finger, M.; Fischer, H.; Franco, C.; du Fresne von Hohenesche, N.; Friedrich, J. M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O. P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmüller, S.; Grasso, A.; Grosse-Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; von Harrach, D.; Hashimoto, R.; Heinsius, F. H.; Herrmann, F.; Hinterberger, F.; Horikawa, N.; d'Hose, N.; -Yu Hsieh, C.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Jörg, P.; Joosten, R.; Kabuß, E.; Ketzer, B.; Khaustov, G. V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J. H.; Kolosov, V. N.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V. F.; Kotzinian, A. M.; Kouznetsov, O.; Krämer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z. V.; Kuchinski, N.; Kunne, F.; Kurek, K.; Kurjata, R. P.; Lednev, A. A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G. K.; Marchand, C.; Martin, A.; Marzec, J.; Matousek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Miyachi, Y.; Nagaytsev, A.; Nagel, T.; Nerling, F.; Neyret, D.; Nikolaenko, V. I.; Novy, J.; Nowak, W.-D.; Nunes, A. S.; Olshevsky, A. G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.-C.; Pereira, F.; Pesek, M.; Peshekhonov, D. V.; Platchkov, S.; Pochodzalla, J.; Polyakov, V. A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Rocco, E.; Rossiyskaya, N. S.; Ryabchikov, D. I.; Rychter, A.; Samoylenko, V. D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I. A.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schönning, K.; Schopferer, S.; Selyunin, A.; Shevchenko, O. Yu.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Sozzi, F.; Srnka, A.; Stolarski, M.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; ter Wolbeek, J.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zink, A.
2016-02-01
New results for the double spin asymmetry A1p and the proton longitudinal spin structure function g1p are presented. They were obtained by the COMPASS Collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH3 target. The data were collected in 2011 and complement those recorded in 2007 at 160 GeV, in particular at lower values of x. They improve the statistical precision of g1p (x) by about a factor of two in the region x ≲ 0.02. A next-to-leading order QCD fit to the g1 world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, ΔΣ, ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of g1p. The uncertainty of ΔΣ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function g1NS (x ,Q2) yields as ratio of the axial and vector coupling constants |gA /gV | = 1.22 ± 0.05 (stat.) ± 0.10 (syst.), which validates the sum rule to an accuracy of about 9%.
Liégeois, Vincent; Champagne, Benoît; Lazzeretti, Paolo
2008-06-28
Two molecular properties, the nuclear electromagnetic hypershielding (psi(gamma,alphabeta) ('I)) and the gradient of the electric dipole-magnetic dipole polarizability (nabla(Igamma)G(alphabeta) (')), have been calculated using the time-dependent Hartree-Fock method. Provided the Hellmann-Feynman theorem is satisfied, these quantities are equivalent and are related through the nabla(Igamma)G(alphabeta) (')=eZ(I)psi(gamma,alphabeta) ('I) relation, where Z(I) is the atomic number of atom I and e the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of G(alphabeta) (') of requiring only the knowledge of nine mixed second-order derivatives of the density matrix with respect to both electric and magnetic fields (D(alpha,beta)(-omega,omega)) instead of the 3N (N is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates (D(Igamma)). It is shown here for the H(2)O(2) molecule that very large basis sets such as the aug-cc-pVQZ or the R12 basis are required to satisfy the Hellmann-Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of G(alphabeta) (') has then been theoretically described and verified for the H(2)O(2) molecule.
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.
D → a1, f1 transition form factors and semileptonic decays via 3-point QCD sum rules
NASA Astrophysics Data System (ADS)
Zuo, Yabing; Hu, Yue; He, Linlin; Yang, Wei; Chen, Yan; Hao, Yannan
2016-07-01
By using the 3-point QCD sum rules, we calculate the transition form factors of D decays into the spin triplet axial vector mesons a1(1260), f1(1285), f1(1420). In the calculations, we consider the quark contents of each meson in detail. In view of the fact that the isospin of a1(1260) is one, we calculate the D+ → a 10(1260) and D0 → a 1‑(1260) transition form factors separately. In the case of f1(1285), f1(1420), the mixing between light flavor SU(3) singlet and octet is taken into account. Based on the form factors obtained here, we give predictions for the branching ratios of relevant semileptonic decays, which can be tested in the future experiments.
NASA Astrophysics Data System (ADS)
Tas, Murat; Tanatar, B.
2008-09-01
We calculate the collective excitation modes of strongly coupled bilayer charged Bose systems. We employ the dielectric matrix formulation to study the correlation effects within the random-phase approximation (RPA), the self consistent field approximation Singwi, Tosi, Land, and Sjölander (STLS), and the quasilocalized charge approximation (QLCA), which satisfies the third-frequency-moment (⟨ω3⟩) sum rule. We find that the QLCA predicts a long-wavelength correlation-induced energy gap in the out-of-phase plasmon mode, similar to the situation in electronic bilayer systems. The energy gap and the plasmon density of states are studied as a function of interlayer separation and coupling parameter rs . The results should be helpful for experimental investigations.
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions. PMID:16321073
Analysis of the strong decay X(5568) → B_s^0π ^+ with QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2016-05-01
In this article, we take the X(5568) to be the scalar diquark-antidiquark type tetraquark state, study the hadronic coupling constant g_{XB_sπ } with the three-point QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension-6 and including both the connected and the disconnected Feynman diagrams; then we calculate the partial decay width of the strong decay X(5568) → B_s^0 π ^+ and obtain the value Γ _X=( 20.5± 8.1) {MeV}, which is consistent with the experimental data Γ _X = ( 21.9 ± 6.4 {}^{+5.0}_{-2.5}) {MeV} from the D0 collaboration.
Radiative decay of the X(3872) as a mixed molecule-charmonium state in QCD sum rules
Nielsen, M.; Zanetti, C. M.
2010-12-01
We use QCD sum rules (QCDSR) to calculate the width of the radiative decay of the meson X(3872), assumed to be a mixture between charmonium and exotic molecular [cq][qc] states with J{sup PC}=1{sup ++}. We find that in a small range for the values of the mixing angle, 5 deg. {<=}{theta}{<=}13 deg., we get the branching ratio {Gamma}(X{yields}J/{psi}{gamma})/{Gamma}(X{yields}J/{psi}{pi}{sup +}{pi}{sup -})=0.19{+-}0.13, which is in agreement, with the experimental value. This result is compatible with the analysis of the mass and decay width of the mode J/{psi}(n{pi}) performed in the same approach.
Fernández-Varea; Garcia-Molina
2000-11-15
Hamaker constants of systems involving liquid water are evaluated, within the full Lifshitz theory, by means of a recently proposed model of the dielectric function of this substance [Dingfelder et al., Radiat. Phys. Chem. 53, 1 (1998)], which has been extended in the present work by including terms corresponding to infrared excitations and microwave relaxation. An important feature of the complete model is that, besides a good fit to experimental data, it satisfies the physical constraint provided by the f sum rule. For symmetrical systems interacting across water, calculated Hamaker constants are generally in good agreement with results obtained using the Ninham-Parsegian representation with the Roth and Lenhoff parameters for water. Copyright 2000 Academic Press.
Analysis of X(5568) as Scalar Tetraquark State in Diquark-Antidiquark Model with QCD Sum Rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2016-09-01
In this article, we take the X(5568) as the diquark-antidiquark type tetraquark state with the spin-parity JP = 0+, construct the scalar-diquark-scalar-antidiquark type current, carry out the operator product expansion up to the vacuum condensates of dimension-10, and study the mass and pole residue in details with the QCD sum rules. We obtain the value MX = (5.57±0.12) GeV, which is consistent with the experimental data. The present prediction favors assigning the X(5568) to be the scalar tetraquark state. Supported by National Natural Science Foundation under Grant No. 11375063, and Natural Science Foundation of Hebei Province under Grant No. A2014502017
Kohut, Sviataslau V; Staroverov, Viktor N
2013-10-28
The exchange-correlation potential of Kohn-Sham density-functional theory, vXC(r), can be thought of as an electrostatic potential produced by the static charge distribution qXC(r) = -(1∕4π)∇(2)vXC(r). The total exchange-correlation charge, QXC = ∫qXC(r) dr, determines the rate of the asymptotic decay of vXC(r). If QXC ≠ 0, the potential falls off as QXC∕r; if QXC = 0, the decay is faster than coulombic. According to this rule, exchange-correlation potentials derived from standard generalized gradient approximations (GGAs) should have QXC = 0, but accurate numerical calculations give QXC ≠ 0. We resolve this paradox by showing that the charge density qXC(r) associated with every GGA consists of two types of contributions: a continuous distribution and point charges arising from the singularities of vXC(r) at each nucleus. Numerical integration of qXC(r) accounts for the continuous charge but misses the point charges. When the point-charge contributions are included, one obtains the correct QXC value. These findings provide an important caveat for attempts to devise asymptotically correct Kohn-Sham potentials by modeling the distribution qXC(r). PMID:24182014
B_c B_c J/ψ vertex form factor at finite temperature in the framework of QCD sum rules approach
NASA Astrophysics Data System (ADS)
Yazici, E.; Sundu, H.; Veliev, E. Veli
2016-02-01
The strong form factor of the Bc BcJ/Ψ vertex is calculated in the framework of the QCD sum rules method at finite temperature. Taking into account additional operators appearing at finite temperature, a thermal Wilson expansion is obtained and QCD sum rules are derived. While increasing the temperature, the strong form factor remains unchanged up to T˜eq 100 MeV but slightly increases after this point. After T˜eq 160 MeV, the form factor suddenly decreases up to T˜eq 170 MeV. The obtained result of the coupling constant by fitting the form factor at Q^2=-m^2_{offshell} at T=0 is in a very good agreement with the QCD sum rules calculations in the case of vacuum. Our prediction can be checked in future experiments.
Kominis, Ioannis
2001-01-31
This thesis presents the results of E-94010, an experiment at Thomas Jefferson National Accelerator Facility (TJNAF) designed to study the spin structure of the neutron at low momentum transfer, and to test the “extended” Gerasimov-Drell-Hearn (GDH) sum rule. The first experiment of its kind, it was performed in experimental Hall-A of TJNAF using a new polarized 3He facility. It has recently been shown that the GDH sum rule and the Bjorken sum rule are both special examples of a more general sum rule that applies to polarized electron scattering off nucleons. This generalized sum rule, due to Ji and Osborne, reduces to the GDH sum rule at Q2 = 0 and to the Bjorken sum rule at Q2 >> 1 GeV2. By studying the Q2 evolution of the extended GDH sum, one learns about the transition from quark-like behavior to hadronic-like behavior. We measured inclusive polarized cross sections by scattering high energy polarized electrons off the new TJNAF polarized 3He target with both longitudinal and transverse target orientations. The high density 3He target, based on optical pumping and spin exchange, was used as an effective neutron target. The target maintained a polarization of about 35% at beam currents as high as 151tA. We describe the precision 3He polarimetry leading to a systematic uncertainty of the target polarization of 4% (relative). A strained GaAs photocathode was utilized in the polarized electron gun, which provided an electron beam with a polarization of about 70%, known to 3% (relative). By using six different beam energies (between 0.86 and 5.06 GeV) and a fixed scattering angle of 15.5°, a wide kinematic coverage was achieved, with 0.02 GeV2< Q2 <1 GcV2 and 0.5 GeV< W < 2.5 GeV for the squared momentum transfer and invariant mass, respectively. From the measured cross sections we extract the 3He spin structure functions He and g1e Finally, we determine the extended GDH sum for the range 0.1 GeV2< Q2 <1 GeV2 for 3He and the neutron.
Gubler, Philipp; Yamamoto, Naoki; Hatsuda, Tetsuo; Nishida, Yusuke
2015-05-15
Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.
A sum rule for the Cabibo mixing t bar V sub us t bar in the three-step quark-mass generation model
Koide. Y., . Dept. of Physics)
1991-09-28
In this paper, from a matrix-form-independent study of 3 {times} 3 quark mass matrices provided through hierarchical three-step mass-generations, a sum rule is derived. In particular, under some conditions, the sum rule leads to the well known relation {vert bar} V {sub us}{vert bar}{approx equal}{vert bar}{radical} m{sub d}/m{sub c} {minus} e{sup i{phi}} {radical} m{sub d}/m{sub d} {vert bar}.
Precision calculation of threshold πd scattering, πN scattering lengths, and the GMO sum rule
NASA Astrophysics Data System (ADS)
Baru, V.; Hanhart, C.; Hoferichter, M.; Kubis, B.; Nogga, A.; Phillips, D. R.
2011-12-01
We use chiral perturbation theory (ChPT) to calculate the πd scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) [1], where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a and a. We study isospin-breaking contributions to the three-body part of a due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
NASA Astrophysics Data System (ADS)
Suzuki, Shugo; Ariizumi, Toshihiro; Li, Ming-Fang
2009-07-01
We study the X-ray magnetic circular dichroism (XMCD) spectra at the U M4,5 and N4,5 edges of uranium monochalcogenides, UX where X=S, Se, and Te, examining the applicability of the XMCD sum rules to UX by the fully relativistic full-potential linear-combination-of-atomic-orbitals (LCAO) method based on the density functional theory. To extract the transitions relevant to the sum-rule analysis, we employ the Mulliken population analysis (MPA). Using the MPA, the orbital sum rule is found to be valid to 10-20% for the M4,5 edges and valid to 5-15% for the N4,5 edges. On the other hand, the spin sum rule is found to be valid to 10-20% for the M4,5 edges whereas valid to 30-35% for the N4,5 edges. Furthermore, it is found that the calculated XMCD spectra are consistent with a recent experimental observation that the intensity of the N4,5 XMCD signal is comparable to that of the M4,5 XMCD signal although contradicting a previous theoretical prediction that the XMCD intensity at the N4,5 edges is one order of magnitude smaller than that at the M4,5 edges.
Kontturi, Ville; Silfsten, Pertti; Peiponen, Kai-Erik
2011-07-01
Absorption spectra from colloids containing different concentrations of spherical gold nanoparticles in water were measured with a spectrophotometer. The absorption spectra were used to calculate the number density of nanoparticles (NPs) with the aid of an unconventional finite spectral band f-sum rule applied for gold colloid. Good correlation between the number density of dispersion electrons, obtained from the f-sum rule, and the number density of nanoparticles was found. The effective absolute refractive index of the gold colloid was obtained with the aid of a singly subtractive Kramers-Kronig relation, and in addition the refractive index change due to the nanoparticles was obtained with the aid of a conventional Kramers-Kronig relation. Such optical properties are valuable in studies of light interaction with nanoparticles.
Revisiting the b1π and ρ π decay modes of the 1-+ light hybrid state with light-cone QCD sum rules
NASA Astrophysics Data System (ADS)
Huang, Zhuo-Ran; Jin, Hong-Ying; Steele, T. G.; Zhang, Zhu-Feng
2016-09-01
We study the ρ π and b1π decay modes of the 1-+ light hybrid state within the framework of light-cone QCD sum rules. We use both the tensor current ψ ¯ σμ νψ and the derivative current ψ ¯ D↔ μγ5ψ as interpolating currents to calculate the partial decay width of the b1π decay mode. Comparing the sum rules obtained by using different currents, we obtain Γ (π1→b1π ) =8 - 23 , 32-86 and 52-151 MeV for m1-+=1.6 , 1.8 and 2.0 GeV respectively, which favor the results from the flux tube models and lattice simulations. We also use the tensor current to study the ρ π decay mode, and although an extended stability criterion is needed, our results suggest a small partial decay width.
NASA Astrophysics Data System (ADS)
Liebsch, Ansgar
1985-11-01
It is shown that the use of the random-phase approximation (RPA) to determine the response of a metal surface to a static uniform external field in conjunction with a local-density description of exchange and correlation in the ground state violates the exact force sum rule. As a result, the static image plane is located considerably closer to the surface and the external field is less effectively screened than in a consistent treatment of exchange and correlation in both ground state and response. In addition, this implementation of the RPA violates the so-called surface f-sum rule, giving a too low number of electrons available for excitation near a metal surface. As a consequence of these violations, the first and first-inverse frequency moment of the imaginary part of the dynamic induced charge as well as its small-frequency behavior are incorrectly described.
Aspects of QCD current algebra on a null plane
NASA Astrophysics Data System (ADS)
Beane, S. R.; Hobbs, T. J.
2016-09-01
Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial-vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial-vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler-Weisberger, Gerasimov-Drell-Hearn, Cabibbo-Radicati and Fubini-Furlan-Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S-matrix elements in the Regge limit.
NASA Astrophysics Data System (ADS)
Cvetič, Gorazd; Kataev, A. L.
2016-07-01
We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.
Application of the QCD light cone sum rule to tetraquarks: The strong vertices XbXbρ and XcXcρ
NASA Astrophysics Data System (ADS)
Agaev, S. S.; Azizi, K.; Sundu, H.
2016-06-01
The full version of the QCD light-cone sum rule method is applied to tetraquarks containing a single heavy b or c quark. To this end, investigations of the strong vertices XbXbρ and XcXcρ are performed, where Xb=[s u ][b ¯ d ¯ ] and Xc=[s u ][c ¯d ¯] are the exotic states built of four quarks of different flavors. The strong coupling constants GXbXbρ and GXcXcρ corresponding to these vertices are found using the ρ -meson leading- and higher-twist distribution amplitudes. In the calculations, Xb and Xc are treated as scalar bound states of a diquark and antidiquark.
Jeffries, J R; Moore, K T; Butch, N P; Maple, M B
2010-05-19
We examine the degree of 5f electron localization in URu{sub 2}Si{sub 2} using spin-orbit sum rule analysis of the U N{sub 4,5} (4d {yields} 5f) edge. When compared to {alpha}-U metal, US, USe, and UTe, which have increasing localization of the 5f states, we find that the 5f states of URu{sub 2}Si{sub 2} are more localized, although not entirely. Spin-orbit analysis shows that intermediate coupling is the correct angular momentum coupling mechanism for URu{sub 2}Si{sub 2} when the 5f electron count is between 2.6 and 2.8. These results have direct ramifications for theoretical assessment of the hidden order state of URu{sub 2}Si{sub 2}, where the degree of localization of the 5f electrons and their contribution to the Fermi surface are critical.
Moore, K; der Laan, G v; Haire, R; Wall, M; Schwartz, A
2005-10-07
Transmission electron microscopy is used to acquire electron energy-loss spectra from phase-specific regions of Pu and U metal, PuO{sub 2} and UO{sub 2}, and aged, self-irradiated Pu metal. The N{sub 4,5} (4d {yields} 5f) spectra are analyzed using the spin-orbit sum rule. Our results show that the technique is sensitive enough to detect changes in the branching ratio of the white-line peaks between the metal and dioxide of both U and Pu. There is a small change in the branching ratio between different Pu metals, and the data trends as would be expected for varying f electron localization, i.e., {alpha}-Pu, {delta}-Pu, aged {delta}-Pu. Moreover, our results suggest that the metal-oxide bonds in UO{sub 2} and PuO{sub 2} are strongly covalent in nature and do not exhibit an integer valence change as would be expected from purely ionic bonding.
NASA Astrophysics Data System (ADS)
Mikhailov, S. V.; Stefanis, N. G.
2009-11-01
The transition pion-photon form factor is studied within the framework of light-cone QCD sum rules. The spectral density for the next-to-leading order corrections is calculated for any Gegenbauer harmonic. At the level of the next-to-next-to-leading order (NNLO) radiative corrections, only that part of the hard-scattering amplitude is included that is proportional to the β-function, taking into account the leading zeroth-order harmonic. The relative size of the NNLO contribution in the prediction for the form factor Fγπ(Q) has been analyzed, making use of the BLM scale-setting procedure. In addition, predictions for the form factor Fρπ are obtained that turn out to be sensitive to the endpoint behavior of the pion distribution amplitude, thus providing in connection with experimental data an additional adjudicator for the pion distribution amplitude. In a note added, we comment on the preliminary high- Q BaBar data on Fγπ arguing that the significant growth of the form factor between 10 and 40 GeV cannot be explained in terms of higher-order perturbative corrections at the NNLO.
Lvov, A.I.; Scopetta, S. |; Drechsel, D.; Scherer, S.
1998-01-01
Photoproduction of e{sup +}e{sup {minus}} pairs at small angles is investigated as a tool to determine the functions f{sub 1} and f{sub 2} entering the real-photon forward Compton scattering amplitude. The method is based on an interference of the Bethe-Heitler and the virtual Compton scattering mechanisms, generating an azimuthal asymmetry in the e{sup +} versus e{sup {minus}} yield. The general case of a circularly polarized beam and a longitudinally polarized target allows one to determine both the real and imaginary parts of f{sub 1} as well as f{sub 2}. The imaginary part of f{sub 2} requires target polarization only. We calculate cross sections and asymmetries of the reaction p({gamma},e{sup +}e{sup {minus}})p, estimate corrections and backgrounds, and propose suitable kinematical regions to perform the experiment. Our investigation shows that photoproduction of e{sup +}e{sup {minus}}-pairs off the proton and light nuclei may serve as a rather sensitive test of the validity of the Gerasimov-Drell-Hearn sum rule. {copyright} {ital 1998} {ital The American Physical Society}
Minnaert, P.; Mozrzymas, M.
1998-01-01
It is shown that the universal R matrix in the tensor product of two irreducible representation spaces of the quantum superalgebra U{sub q}{bold (}osp(1{vert_bar}2){bold )} can be expressed by Clebsch{endash}Gordan coefficients. The Racah sum rule satisfied by U{sub q}{bold (}osp(1{vert_bar}2){bold )} Racah coefficients and 6{minus}j symbols is derived from the properties of the universal R matrix in the tensor product of three representation spaces. Considering the tensor product of four irreducible representations, it is shown that Biedenharn{endash}Elliott identity holds for U{sub q}{bold (}osp(1{vert_bar}2){bold )} Racah coefficients and 6{minus}j symbols. A recursion relation for U{sub q}{bold (}osp(1{vert_bar}2){bold )} 6{minus}j symbols is derived from the Biedenharn{endash}Elliott identity. {copyright} {ital 1998 American Institute of Physics.}
Levchuk, M. I.
2010-10-15
Helicity-dependent incoherent pion photoproduction in the reaction {gamma}-vectord-vector{yields}{pi}NN is studied in the framework of the diagrammatic approach. Contributions to the reaction amplitude from diagrams corresponding to impulse approximation as well as NN and {pi}N interactions in the final state have been evaluated. The elementary {gamma}N{yields}{pi}N operator is taken from the MAID and SAID models. A detailed comparison of the predictions with recent experimental data by the GDH and A2 collaborations at energies below 500 MeV is presented. Reasonable agreement with the data on the yields and cross sections for the polarized beam and polarized target has been achieved in all channels. The unpolarized data of the GDH and A2 collaborations have also been analyzed within the approach. A strong overestimation for the neutral channel has been found. At the same time, the model provides a quite satisfactory description of the unpolarized data for the charged channels. The sensitivity of the obtained results to the choice of the elementary {gamma}N{yields}{pi}N operator is discussed in detail. The contribution of the {gamma}d{yields}{pi}NN reaction to the GDH sum rule for the deuteron up to a photon energy of 1.65 GeV has been evaluated with the result of 235{+-}25 {mu}b.
Ball, P. )
1993-10-01
We investigate the semileptonic decays of [ital B] and [ital D] mesons into [pi] and [rho] mesons, respectively, by means of QCD sum rules. We find that for the vector form factors involved the pole dominance hypothesis is valid to good accuracy with pole masses in the expected range. Pole dominance, however, does not apply to the axial form factors which results in specific predictions for the predominant polarization of the [rho] meson and the shape of the lepton spectrum. For the total decay rates we find [Gamma]([ital [bar B
The ρ(1S, 2S), ψ(1S, 2S), Υ(1S, 2S) and ψ t (1S, 2S) Mesons in a Double Pole QCD Sum Rule
NASA Astrophysics Data System (ADS)
Maior de Sousa, M. S.; da Silva, R. Rodrigues
2016-09-01
We use the method of double pole QCD sum rule, which is basically a fit with two exponentials of the correlation function, where we can extract the masses and decay constants of mesons as a function of the Borel mass. We apply this method to study the mesons: ρ(1S,2S), ψ(1S,2S), Υ(1S,2S), and ψ t (1S,2S). We also present predictions for the toponiuns masses ψ t (1S,2S) of m(1S)=357 GeV and m(2S)=374 GeV.
Sundu, Hayriye; Bayar, Melahat; Azizi, Kazem
2010-12-22
The form factors of the semileptonic B{sub c{yields}}S(AV)l{nu} (l = {tau},{mu},e) transitions, where S and AV denote the scalar {Chi}{sub c0} and axial vector ({Chi}{sub c1},h{sub c}) mesons, are calculated within the framework of the three-point QCD sum rules. The results of form factors are used to estimate the total decay widths and branching ratios of these transitions. A comparison of our results on branching ratios with the predictions of other approaches is also presented.
NASA Astrophysics Data System (ADS)
Hiyama, E.; Gibson, B. F.; Kamimura, M.
2004-09-01
4He possesses a second 0+ state; the transition form factor has been measured via inelastic electron scattering. The nature of the 0+2 state’s spatial structure has been controversial. An accurate four-nucleon calculation utilizing a realistic NN force (Argonne V 8' ) plus phenomenological NNN three-body force has been performed for both the 4He ground state and second 0+ state ( Ex =20.21 MeV) using the Gaussian expansion method. The calculated one-body densities and transition density show a significant difference between the states. The resulting impulse approximation transition form factor 4He (e, e' ) 4He ( 0+2 ) agrees with the available data. The overlap of the 0+2 wave function with the trinucleon ground state suggests that the structure is primarily a loosely bound 3N+N system and not a breathing mode. It is found that a major part of the energy-weighted E0 sum rule value is exhausted by nonresonant, low-energy continuum states other than the second 0+ state, in contrast to heavier nuclei where a dominant fraction of the sum-rule limit is exhausted by the second 0+ state because it corresponds to a collective, breathing mode.
Gan Longfei; Huang Mingqiu
2010-09-01
We present an analysis of semileptonic decays of orbitally, P-wave excited B{sub s} meson states B{sub s}**, including the newly found narrow B{sub s1}(5830) and B{sub s2}*(5840) states, into low-lying D{sub s} mesons (D{sub s}(1968), D{sub s}*(2112), D{sub sJ}(2317), D{sub sJ}(2460)) within the framework of the heavy quark effective theory. The relevant universal form factors are estimated using QCD sum rules at the leading order of the heavy quark expansion. The decay widths are predicted and the branching ratios are estimated.
Djawotho, Pibero
2002-12-01
This dissertation presents results of experiment E94-010 performed at Jefferson Laboratory (simply known as JLab) in Hall A. The experiment aimed to measure the low Q^{2} evolution of the Gerasimov-Drell-Hearn (GDH) integral from Q^{2} = 0.1 to 0.9 GeV^{2}. The GDH sum rule at the real photon point provides an important test of Quantum Chromodynamics (QCD). The low Q^{2} evolution of the GDH integral contests various resonance models, Chiral Perturbation Theory ({chi} PT) and lattice QCD calculations, but more importantly, it helps us understand the transition between partonic and hadronic degrees of freedom. At high Q^{2}, beyond 1 GeV^{2}, the difference of the GDH integrals for the proton and the neutron is related to the Bjorken sum rule, another fundamental test of QCD. In addition, results of the measurements for the spin structure functions g_{1} and g_{2}, cross sections, and asymmetries are presented. E94-010 was the first experiment of its kind at JLab. It used a high-pressure, polarized ^{3}He target with a gas pressure of 10 atm and average target polarization of 35%. For the first time, the polarized electron source delivered an average beam polarization of 70% with a beam current of 15 micro A. The limit on the beam current was only imposed by the target. The experiment required six different beam energies from 0.86 to 5.1 GeV. This was the first time the accelerator ever reached 5.1 GeV. Both High-Resolution Spectrometers of Hall A, used in singles mode, were positioned at 15.5 ° each.
NASA Astrophysics Data System (ADS)
Blümlein, Johannes; Falcioni, Giulio; De Freitas, Abilio
2016-09-01
We calculate analytically the flavor non-singlet O (αs2) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F1,2,Lep (x ,Q2) and g1,2ep (x ,Q2) and charged current non-singlet structure functions F1,2,3ν (ν bar) p (x ,Q2), at general virtualities Q2 in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q2 and the effects of the power corrections due to the heavy quark mass are of the size of the known O (αs4) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q2 ≫mc,b2. We also study the target mass corrections to the above sum rules.
Zhang, J.-Z.; Dyson, A.; Ridley, B. K.
2015-01-14
Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation (ER) of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation (PD) and ER time due to both half-space and interface phonons are calculated as functions of the electron temperature T{sub e} using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby, particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: With no hot phonons or screening, the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for ER time with the two phonon models (within a 5% of deviation). However, the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the PD values obtained from the DC and 3DP models are in general different in the spontaneous phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register's scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the ER: their contribution is enhanced in the spontaneous emission process but is dramatically reduced after including the HPE. Our calculation with both
ERIC Educational Resources Information Center
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
Experimental study of isovector spin sum rules
Alexandre Deur; Peter Bosted; Volker Burkert; Donald Crabb; Kahanawita Dharmawardane; Gail Dodge; Tony Forest; Keith Griffioen; Sebastian Kuhn; Ralph Minehart; Yelena Prok
2008-02-04
We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05<2.92$ GeV$^2$. The integral is fit to extract the twist-4 element $f_{2}^{p-n}$ which is large and negative. Systematic studies of this higher twist analysis establish its legitimacy at $Q^{2}$ around 1 GeV$^{2}$. We also extracted the isovector part of the generalized forward spin polarizability $\\gamma_{0}$. Although this quantity provides a robust test of Chiral Perturbation Theory, our data disagree with the calculations.
Ghahramany, N.; Khosravi, R.
2009-07-01
We investigate the rare semileptonic decays B{sub s}{yields}[f{sub 0}(980),K{sub 0}*(1430)]l{sup +}l{sup -}, (l=e, {mu}, {tau}), and B{sub s}{yields}[f{sub 0}(980),K{sub 0}*(1430)]{nu}{nu} in the framework of the three-point QCD sum rules. These decays are important to study because the f{sub 0}(980) and K{sub 0}*(1430) are the scalar mesons with total spin 0 and even parity and the quark content of them are still controversial in high energy physics. These rare decays occur at loop level by electroweak penguin and weak box diagrams in the standard model via the flavor changing neutral current transitions of b{yields}d, s, and not allowed by tree level. Considering the effective contributions of the nonperturbative parts of the correlation function, we calculate the relevant form factors of these transitions. The branching fractions and longitudinal lepton polarization asymmetry are also investigated.
ERIC Educational Resources Information Center
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
NASA Astrophysics Data System (ADS)
Fu, Hai-Bing; Wu, Xing-Gang; Ma, Yang; Cheng, Wei; Zhong, Tao
2016-08-01
We present a detailed calculation on the B\\to {K}* transition form factors (TFFs), {A}{0,1,2}, V and {T}{1,2,3}, within the QCD light-cone sum rules (LCSRs). To suppress the contributions from high-twist light-cone distribution amplitudes, we adopt a right-handed chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leading-twist distribution amplitude {φ }2;{K*}\\perp provides over 90% contribution, thus those TFFs provide good platforms for testing the property of {φ }2;{K*}\\perp . We suggest a model for {φ }2;{K*}\\perp , in which two parameters {B}2;{K*}\\perp and {C}2;{K*}\\perp dominantly control its longitudinal distribution. With a proper choice of {B}2;{K*}\\perp and {C}2;{K*}\\perp , our predictions on B\\to {K}* TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the B-meson rare decay B\\to {K}*{μ }+{μ }-. The predicted differential branching fraction {{d}}{B}/{{d}}{q}2(B\\to {K}*{μ }+{μ }-) is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable q 2-region, we get the branching fraction, {B}(B\\to {K}*{μ }+{μ }-)=≤ft({1.088}-0.205+0.261\\right)× {10}-6, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of {φ }2;{K*}\\perp .
Summing pressure compensation control
Myers, H.A.
1988-04-26
This patent describes a summing pressure compensator control for hydraulic loads with at least one of the hydraulic loads being a variable displacement motor having servo means for controlling the displacement thereof, first hydraulic means responsive to the supply of fluid to the variable displacement motor to provide a first pressure signal, second hydraulic means responsive to the supply of fluid to a second hydraulic load to provide a second pressure signal, summing means for receiving the first and second pressure signals and providing a control signal proportional to the sum of the first and second pressure signals, the control signal being applied to the servo means to increase the displacement of the variable displacement motor.
NASA Technical Reports Server (NTRS)
Robertson, G.
1982-01-01
Calibration was performed on the shuttle upper atmosphere mass spectrometer (SUMS). The results of the calibration and the as run test procedures are presented. The output data is described, and engineering data conversion factors, tables and curves, and calibration on instrument gauges are included. Static calibration results which include: instrument sensitive versus external pressure for N2 and O2, data from each scan of calibration, data plots from N2 and O2, and sensitivity of SUMS at inlet for N2 and O2, and ratios of 14/28 for nitrogen and 16/32 for oxygen are given.
Structure-property correlation study through sum-over-state approach
NASA Astrophysics Data System (ADS)
Nandi, P. K.; Hatua, K.; Bansh, A. K.; Panja, N.; Ghanty, T. K.
2015-01-01
The use of Thomas Kuhn (TK) sum rule in the expanded sum-over-state (SOS) expression of hyperpolarizabilities leads to various relationships between different order of polarizabilities and ground state dipole moment etc.
Counting Triangles to Sum Squares
ERIC Educational Resources Information Center
DeMaio, Joe
2012-01-01
Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.
Darmann, Andreas; Nicosia, Gaia; Pferschy, Ulrich; Schauer, Joachim
2014-01-01
In this work we address a game theoretic variant of the Subset Sum problem, in which two decision makers (agents/players) compete for the usage of a common resource represented by a knapsack capacity. Each agent owns a set of integer weighted items and wants to maximize the total weight of its own items included in the knapsack. The solution is built as follows: Each agent, in turn, selects one of its items (not previously selected) and includes it in the knapsack if there is enough capacity. The process ends when the remaining capacity is too small for including any item left. We look at the problem from a single agent point of view and show that finding an optimal sequence of items to select is an NP-hard problem. Therefore we propose two natural heuristic strategies and analyze their worst-case performance when (1) the opponent is able to play optimally and (2) the opponent adopts a greedy strategy. From a centralized perspective we observe that some known results on the approximation of the classical Subset Sum can be effectively adapted to the multi-agent version of the problem. PMID:25844012
ERIC Educational Resources Information Center
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
Small sum privacy and large sum utility in data publishing.
Fu, Ada Wai-Chee; Wang, Ke; Wong, Raymond Chi-Wing; Wang, Jia; Jiang, Minhao
2014-08-01
While the study of privacy preserving data publishing has drawn a lot of interest, some recent work has shown that existing mechanisms do not limit all inferences about individuals. This paper is a positive note in response to this finding. We point out that not all inference attacks should be countered, in contrast to all existing works known to us, and based on this we propose a model called SPLU. This model protects sensitive information, by which we refer to answers for aggregate queries with small sums, while queries with large sums are answered with higher accuracy. Using SPLU, we introduce a sanitization algorithm to protect data while maintaining high data utility for queries with large sums. Empirical results show that our method behaves as desired.
Energy-weighted sum rules, y-scaling and duality
J. Wallace Van Orden; Sabine Jeschonnek
2002-09-01
The phenomena of scaling and Bloom-Gilman duality are examined in the context of simple nonrelativistic and relativistic quantum mechanical models. These models are shown to scale and to show the qualitative feature of Bloom-Gilman duality. This suggests that these phenomena do not necessarily require the properties of QCD.
Direct Sum Decomposition of Groups
ERIC Educational Resources Information Center
Thaheem, A. B.
2005-01-01
Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…
Summing Planar Bosonic Open Strings
Bardakci, Korkut
2006-02-16
In earlier work, planar graphs of massless {phi}{sup 3} theory were summed with the help of the light cone world sheet picture and the mean field approximation. In the present article, the same methods are applied to the problem of summing planar bosonic open strings. They find that in the ground state of the system, string boundaries form a condensate on the world sheet, and a new string emerges from this summation. Its slope is always greater than the initial slope, and it remains non-zero even when the initial slope is set equal to zero. If they assume the initial string tends to a field a theory in the zero slope limit, this result provides evidence for string formation in field theory.
Note on cyclic sum and combination sum of color-ordered gluon amplitudes
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Feng, Bo; Fu, Chih-Hao
2012-03-01
Continuing our previous study [22] of permutation sum of color ordered tree amplitudes of gluons, in this note, we prove the large- z behavior of their cyclic sum and the combination of cyclic and permutation sums under BCFW deformation. Unlike the permutation sum, the study of cyclic sum and the combination of cyclic and permutation sums is much more difficult. By using the generalized Bern-Carrasco-Johansson (BCJ) relation, we have proved the boundary behavior of cyclic sum with nonadjacent BCFW deformation. The proof of cyclic sum with adjacent BCFW deformation is a little bit simpler, where only Kleiss-Kuijf (KK) relations are needed. Finally we have presented a new observation for partial-ordered permutation sum and applied it to prove the boundary behavior of combination sum with cyclic and permutation.
Sinha, Urbasi
2011-09-23
This paper is based on work published in [1]. It describes a triple slit experiment using single photons that has been used to provide a bound on one of the most fundamental axioms of quantum mechanics i.e. Born's rule for probabilities [2]. In spite of being one of the most successful theories which describes various natural phenomena, quantum mechanics has enough intricacies and ''weirdness'' associated with it which makes many physicists believe that it may not be the final theory and hints towards the possibility of more generalized versions. Quantum interference as shown by a double slit diffraction experiment only occurs from pairs of paths. Even in multi-slit versions, interference can only occur between pairs of possibilities and increasing the number of slits does not increase the complexity of the theory that still remains second-order. However, more generalized versions of quantum mechanics may allow for multi-path i.e. higher than second order interference. This experiment also provides a bound on the magnitude of such higher order interference. We have been able to bound the magnitude of three-path interference to less than 10{sup -2} of the expected two-path interference, thus ruling out third and higher order interference and providing a bound on the accuracy of Born's rule.
NASA Astrophysics Data System (ADS)
Sinha, Urbasi
2011-09-01
This paper is based on work published in [1]. It describes a triple slit experiment using single photons that has been used to provide a bound on one of the most fundamental axioms of quantum mechanics i.e. Born's rule for probabilities [2]. In spite of being one of the most successful theories which describes various natural phenomena, quantum mechanics has enough intricacies and "weirdness" associated with it which makes many physicists believe that it may not be the final theory and hints towards the possibility of more generalized versions. Quantum interference as shown by a double slit diffraction experiment only occurs from pairs of paths. Even in multi-slit versions, interference can only occur between pairs of possibilities and increasing the number of slits does not increase the complexity of the theory that still remains second-order. However, more generalized versions of quantum mechanics may allow for multi-path i.e. higher than second order interference. This experiment also provides a bound on the magnitude of such higher order interference. We have been able to bound the magnitude of three-path interference to less than 10-2 of the expected two-path interference, thus ruling out third and higher order interference and providing a bound on the accuracy of Born's rule.
Where Does Latin "Sum" Come From?
ERIC Educational Resources Information Center
Nyman, Martti A.
1977-01-01
The derivation of Latin "sum,""es(s),""est" from Indo-European "esmi,""est,""esti" involves methodological problems. It is claimed here that the development of "sum" from "esmi" is related to the origin of the variation "est-st" (less than"esti"). The study is primarily concerned with this process, but chronological suggestions are also made. (CHK)
Item Response Modeling with Sum Scores
ERIC Educational Resources Information Center
Johnson, Timothy R.
2013-01-01
One of the distinctions between classical test theory and item response theory is that the former focuses on sum scores and their relationship to true scores, whereas the latter concerns item responses and their relationship to latent scores. Although item response theory is often viewed as the richer of the two theories, sum scores are still…
Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe
2015-01-01
We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat–Kolchin–Ribet criterion, in a form that is easily applicable in analytic number theory. PMID:25802414
40 CFR 91.508 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2010 CFR
2010-07-01
... Equation must be final deteriorated test results as defined in § 91.509(c). Ci = max Where: Ci = The current CumSum statistic Ci-1 = The previous CumSum statistic. Prior to any testing, the CumSum statistic... Limit F = 0.25 × σ After each test, Ci is compared to the action limit, H, the quantity which the...
Robey, Robert
2015-10-06
This code is a set of global sums to support the paper "Computational Reproducibility for Production Physics Applications" submitted to the Numerical Reproducibility at Exascale (NRE 2015) workshop at the 2015 Supercomputing conference, Nov. 20, 2015
Support activities to maintain SUMS flight readiness
NASA Technical Reports Server (NTRS)
Wright, Willie
1992-01-01
The Shuttle Upper Atmosphere Mass Spectrometer (SUMS), a component experiment of the NASA Orbital Experiments Program (OEX), was flown aboard the shuttle Columbia (OV102) mounted at the forward end of the nose landing gear well with an atmospheric gas inlet system fitted to the lower fuselage (chin panel) surface. The SUMS was designed to provide atmospheric data in flow regimes inaccessible prior to the development of the Space Transportation System (STS). The experiment mission operation began about one hour prior to shuttle de-orbit entry maneuver and continued until reaching 1.6 torr (about 86 km altitude). The SUMS mass spectrometer consists of the spare unit from the Viking mission to Mars. Bendix Aerospace under contract to NASA LaRC incorporated the Viking mass spectrometer, a microprocessor based logic card, a pressurized instrument case, and the University of Texas at Dallas provided a gas inlet system into a configuration suited to interface with the shuttle Columbia. The SUMS experiment underwent static and dynamic calibration as well as vacuum maintenance before and after STS 40 shuttle flight. The SUMS flew a total of 3 times on the space shuttle Columbia. Between flights the SUMS was maintained in flight ready status. The flight data has been analyzed by the NASA LaRC Aerothermodynamics Branch. Flight data spectrum plots and reports are presented in the Appendices to the Final Technical Report for NAS1-17399.
Experimental results of the betatron sum resonance
Wang, Y.; Ball, M.; Brabson, B.
1993-06-01
The experimental observations of motion near the betatron sum resonance, {nu}{sub x} + 2{nu}{sub z} = 13, are presented. A fast quadrupole (Panofsky-style ferrite picture-frame magnet with a pulsed power supplier) producing a betatron tune shift of the order of 0.03 at rise time of 1 {mu}s was used. This quadrupole was used to produce betatron tunes which jumped past and then crossed back through a betatron sum resonance line. The beam response as function of initial betatron amplitudes were recorded turn by turn. The correlated growth of the action variables, J{sub x} and J{sub z}, was observed. The phase space plots in the resonance frame reveal the features of particle motion near the nonlinear sum resonance region.
40 CFR 90.708 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2010 CFR
2010-07-01
... i -1+X i−(FEL+F))] Where: Ci=The current CumSum statistic. Ci -1=The previous CumSum statistic... to paragraph (a)(1) of this section, Ci is compared to the action limit, H, the quantity which...
The Visual Interactive Computer-Aided Approach to Teaching Zero-Sum/Nonzero-Sum Games.
ERIC Educational Resources Information Center
Shim, J. P.
1988-01-01
Discusses the use of the microcomputer as an instructional tool in the domain of competitive decision making. Describes how visual interactive zero-sum/nonzero-sum games can be useful in teaching this subject. Compares student performances based on the visual interactive approach to those of traditional approaches. (GEA)
40 CFR 90.708 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2012 CFR
2012-07-01
... i −1+X i−(FEL+F))] Where: Ci=The current CumSum statistic. Ci -1=The previous CumSum statistic... individual engine. FEL=Family Emission Limit (the standard if no FEL). F=.25×σ. (2) After each test pursuant... configuration, or the use of a different deterioration factor) with no changes to the FEL (where...
40 CFR 90.708 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2013 CFR
2013-07-01
... i −1+X i−(FEL+F))] Where: Ci=The current CumSum statistic. Ci -1=The previous CumSum statistic... individual engine. FEL=Family Emission Limit (the standard if no FEL). F=.25×σ. (2) After each test pursuant... configuration, or the use of a different deterioration factor) with no changes to the FEL (where...
40 CFR 90.708 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... i -1+X i−(FEL+F))] Where: Ci=The current CumSum statistic. Ci -1=The previous CumSum statistic... individual engine. FEL=Family Emission Limit (the standard if no FEL). F=.25×σ. (2) After each test pursuant... configuration, or the use of a different deterioration factor) with no changes to the FEL (where...
40 CFR 90.708 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2014 CFR
2014-07-01
... i −1+X i−(FEL+F))] Where: Ci=The current CumSum statistic. Ci -1=The previous CumSum statistic... individual engine. FEL=Family Emission Limit (the standard if no FEL). F=.25×σ. (2) After each test pursuant... configuration, or the use of a different deterioration factor) with no changes to the FEL (where...
Summing threshold logs in a parton shower
NASA Astrophysics Data System (ADS)
Nagy, Zoltán; Soper, Davison E.
2016-10-01
When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in α s that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.
Sums of Integer Squares: A New Look.
ERIC Educational Resources Information Center
Sastry, K. R. S.; Pranesachar, C. R.; Venkatachala, B. J.
1998-01-01
Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)
Fibonacci Identities via the Determinant Sum Property
ERIC Educational Resources Information Center
Spivey, Michael
2006-01-01
We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.
A 2-categorical state sum model
Baratin, Aristide; Freidel, Laurent
2015-01-15
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027–2060 (2007)] which was shown to lead after gauge-fixing to Korepanov’s invariant of 4-manifolds.
A 2-categorical state sum model
NASA Astrophysics Data System (ADS)
Baratin, Aristide; Freidel, Laurent
2015-01-01
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027-2060 (2007)] which was shown to lead after gauge-fixing to Korepanov's invariant of 4-manifolds.
Lattice sums arising from the Poisson equation
NASA Astrophysics Data System (ADS)
Bailey, D. H.; Borwein, J. M.; Crandall, R. E.; Zucker, I. J.
2013-03-01
In recent times, attention has been directed to the problem of solving the Poisson equation, either in engineering scenarios (computational) or in regard to crystal structure (theoretical). Herein we study a class of lattice sums that amount to Poisson solutions, namely the n-dimensional forms \\begin{eqnarray*} \\phi _n(r_1, \\dots ,r_n) = \\frac{1}{\\pi ^2} \\sum _{m_1, \\dots , m_n \\ odd} \\frac{e^{i \\pi ( m_1 r_1 + \\cdots + m_n r_n)}}{m_1^2 + \\cdots + m_n^2}. \\end{eqnarray*} By virtue of striking connections with Jacobi ϑ-function values, we are able to develop new closed forms for certain values of the coordinates rk, and extend such analysis to similar lattice sums. A primary result is that for rational x, y, the natural potential ϕ2(x, y) is \\frac{1}{\\pi } log A where A is an algebraic number. Various extensions and explicit evaluations are given. Such work is made possible by number-theoretical analysis, symbolic computation and experimental mathematics, including extensive numerical computations using up to 20 000-digit arithmetic.
Sum Product Networks for Activity Recognition.
Amer, Mohamed R; Todorovic, Sinisa
2016-04-01
This paper addresses detection and localization of human activities in videos. We focus on activities that may have variable spatiotemporal arrangements of parts, and numbers of actors. Such activities are represented by a sum-product network (SPN). A product node in SPN represents a particular arrangement of parts, and a sum node represents alternative arrangements. The sums and products are hierarchically organized, and grounded onto space-time windows covering the video. The windows provide evidence about the activity classes based on the Counting Grid (CG) model of visual words. This evidence is propagated bottom-up and top-down to parse the SPN graph for the explanation of the video. The node connectivity and model parameters of SPN and CG are jointly learned under two settings, weakly supervised, and supervised. For evaluation, we use our new Volleyball dataset, along with the benchmark datasets VIRAT, UT-Interactions, KTH, and TRECVID MED 2011. Our video classification and activity localization are superior to those of the state of the art on these datasets.
SUMS experiment flight results on STS-35
NASA Technical Reports Server (NTRS)
Blanchard, Robert C.; Ozoroski, Thomas A.; Nicholson, John Y.
1993-01-01
Calibrated pressure measurements for species with mass to charge ratios up to 50 amu/e(-) were obtained from the Shuttle Upper Atmosphere Mass Spectrometer (SUMS) experiment during reentry on the STS-35 mission. Data were collected from 180 km, when the signal rose above the background, to about 87 km, when the SUMS system automatically closed the gas inlet value. However, data above 115 km was contaminated from a source of gas emanating from pressure transducers connected in parallel to the mass spectrometer. At lower altitudes, the pressure transducer data is compared with the mass spectrometer total pressure with excellent agreement. The free-stream density in the rarefied flow flight regime is calculated using an orifice pressure coefficient model based upon direct simulation Monte Carlo results. This density, when compared with the 1976 U.S. standard atmosphere model, exhibits the wave-like nature seen on previous flights using accelerometry. In addition, selected spectra are presented at higher altitudes (320 km) showing the effects of the ingestion of gases from a forward fuselage fuel dump. An analysis of the spectra data from this event is presented to show that no significant permanent changes occurred which affected the data interpretation at lower altitudes. Further, the localized chemistry from the individual species during the onset of aerodynamic heating is examined to the extent possible for a closed source system, such as SUMS. Near the orifice entrance, a significant amount of CO2 was generated from chemical reactions with the carbon panels of the Orbiter and absorbed oxygen on the system tubing.
SUMS experiment flight results on STS-35
NASA Astrophysics Data System (ADS)
Blanchard, Robert C.; Ozoroski, Thomas A.; Nicholson, John Y.
1993-04-01
Calibrated pressure measurements for species with mass to charge ratios up to 50 amu/e(-) were obtained from the Shuttle Upper Atmosphere Mass Spectrometer (SUMS) experiment during reentry on the STS-35 mission. Data were collected from 180 km, when the signal rose above the background, to about 87 km, when the SUMS system automatically closed the gas inlet value. However, data above 115 km was contaminated from a source of gas emanating from pressure transducers connected in parallel to the mass spectrometer. At lower altitudes, the pressure transducer data is compared with the mass spectrometer total pressure with excellent agreement. The free-stream density in the rarefied flow flight regime is calculated using an orifice pressure coefficient model based upon direct simulation Monte Carlo results. This density, when compared with the 1976 U.S. standard atmosphere model, exhibits the wave-like nature seen on previous flights using accelerometry. In addition, selected spectra are presented at higher altitudes (320 km) showing the effects of the ingestion of gases from a forward fuselage fuel dump. An analysis of the spectra data from this event is presented to show that no significant permanent changes occurred which affected the data interpretation at lower altitudes. Further, the localized chemistry from the individual species during the onset of aerodynamic heating is examined to the extent possible for a closed source system, such as SUMS. Near the orifice entrance, a significant amount of CO2 was generated from chemical reactions with the carbon panels of the Orbiter and absorbed oxygen on the system tubing.
ERIC Educational Resources Information Center
Onorato, P.
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…
Sum-SINR/sum-capacity optimal multisignature spread-spectrum steganography
NASA Astrophysics Data System (ADS)
Wei, Lili; Pados, Dimitris A.; Batalama, Stella N.; Medley, Michael J.
2008-04-01
For any given digital host image or audio file (or group of hosts) and any (block) transform domain of interest, we find an orthogonal set of signatures that achieves maximum sum-signal-to-interference-plus-noise ratio (sum- SINR) spread-spectrum message embedding for any fixed embedding amplitude values. We also find the sumcapacity optimal amplitude allocation scheme for any given total distortion budget under the assumption of (colored) Gaussian transform-domain host data. The practical implication of the results is sum-SINR, sumcapacity optimal multiuser/multisignature spread-spectrum data hiding in the same medium. Theoretically, the findings establish optimality of the recently presented Gkizeli-Pados-Medley multisignature eigen-design algorithm.
Partial Row-Sums of Pascal's Triangle
ERIC Educational Resources Information Center
Ollerton, Richard L.
2007-01-01
Identities for many and varied combinations of binomial coefficients abound. Indeed, because of the wide range of interrelationships it is possible that a great deal of mathematical effort has been wasted in proving essentially equivalent formulae. As well as proving identities these methods can be used to rule out closed form solutions (at least…
22 CFR 19.13-1 - Lump-sum credit.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Lump-sum credit. 19.13-1 Section 19.13-1... THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM § 19.13-1 Lump-sum credit. “Lump-sum credit” is the compulsory and special contributions to a participant's or former participant's credit in the...
22 CFR 19.13-1 - Lump-sum credit.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 22 Foreign Relations 1 2011-04-01 2011-04-01 false Lump-sum credit. 19.13-1 Section 19.13-1... THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM § 19.13-1 Lump-sum credit. “Lump-sum credit” is the compulsory and special contributions to a participant's or former participant's credit in the...
22 CFR 19.13-1 - Lump-sum credit.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 22 Foreign Relations 1 2013-04-01 2013-04-01 false Lump-sum credit. 19.13-1 Section 19.13-1... THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM § 19.13-1 Lump-sum credit. “Lump-sum credit” is the compulsory and special contributions to a participant's or former participant's credit in the...
5 CFR 831.2004 - Amount of lump-sums.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 5 Administrative Personnel 2 2010-01-01 2010-01-01 false Amount of lump-sums. 831.2004 Section 831.2004 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED) CIVIL SERVICE REGULATIONS (CONTINUED) RETIREMENT Payment of Lump Sums § 831.2004 Amount of lump-sums. If applicable, the amount of...
Interpreting the Four Types of Sums of Squares in SPSS.
ERIC Educational Resources Information Center
Tanguma, Jesus; Speed, F. M.
This paper analyzes three possible research designs using each of the four types of sums of squares in the Statistical Package for the Social Sciences (SPSS). When the design is balanced (i.e., each cell has the same number of observations), all of the SPSS types of sums of squares yield equivalent results (testable hypotheses and sums of squares)…
29 CFR 4050.8 - Automatic lump sum.
Code of Federal Regulations, 2010 CFR
2010-07-01
... determined under § 4050.5(a)(1) (mandatory lump sum) or § 4050.5(a)(2) (de minimis lump sum). (a) General... the deemed distribution date, to the missing participant's estate. (b) De minimis annuity alternative... under § 4050.5(a)(2) (de minimis lump sum) (or the guaranteed benefit form for a beneficiary of such...
Rates of profit as correlated sums of random variables
NASA Astrophysics Data System (ADS)
Greenblatt, R. E.
2013-10-01
Profit realization is the dominant feature of market-based economic systems, determining their dynamics to a large extent. Rather than attaining an equilibrium, profit rates vary widely across firms, and the variation persists over time. Differing definitions of profit result in differing empirical distributions. To study the statistical properties of profit rates, I used data from a publicly available database for the US Economy for 2009-2010 (Risk Management Association). For each of three profit rate measures, the sample space consists of 771 points. Each point represents aggregate data from a small number of US manufacturing firms of similar size and type (NAICS code of principal product). When comparing the empirical distributions of profit rates, significant ‘heavy tails’ were observed, corresponding principally to a number of firms with larger profit rates than would be expected from simple models. An apparently novel correlated sum of random variables statistical model was used to model the data. In the case of operating and net profit rates, a number of firms show negative profits (losses), ruling out simple gamma or lognormal distributions as complete models for these data.
40 CFR 91.508 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2012 CFR
2012-07-01
... = 0 (i.e. C0 = 0) Xi = The current emission test result for an individual engine FEL = Family Emission... different deterioration factor) with no changes to the FEL, all previous sample size and CumSum statistic... § 91.122 by modifying its FEL as a result of an engine family modification, the manufacturer...
40 CFR 91.508 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2014 CFR
2014-07-01
... = 0 (i.e. C0 = 0) Xi = The current emission test result for an individual engine FEL = Family Emission... different deterioration factor) with no changes to the FEL, all previous sample size and CumSum statistic... § 91.122 by modifying its FEL as a result of an engine family modification, the manufacturer...
40 CFR 91.508 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2013 CFR
2013-07-01
... = 0 (i.e. C0 = 0) Xi = The current emission test result for an individual engine FEL = Family Emission... different deterioration factor) with no changes to the FEL, all previous sample size and CumSum statistic... § 91.122 by modifying its FEL as a result of an engine family modification, the manufacturer...
40 CFR 91.508 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... = 0 (i.e. C0 = 0) Xi = The current emission test result for an individual engine FEL = Family Emission... different deterioration factor) with no changes to the FEL, all previous sample size and CumSum statistic... § 91.122 by modifying its FEL as a result of an engine family modification, the manufacturer...
Evans, Philip; Wolf, Bob
2005-01-01
Corporate leaders seeking to boost growth, learning, and innovation may find the answer in a surprising place: the Linux open-source software community. Linux is developed by an essentially volunteer, self-organizing community of thousands of programmers. Most leaders would sell their grandmothers for workforces that collaborate as efficiently, frictionlessly, and creatively as the self-styled Linux hackers. But Linux is software, and software is hardly a model for mainstream business. The authors have, nonetheless, found surprising parallels between the anarchistic, caffeinated, hirsute world of Linux hackers and the disciplined, tea-sipping, clean-cut world of Toyota engineering. Specifically, Toyota and Linux operate by rules that blend the self-organizing advantages of markets with the low transaction costs of hierarchies. In place of markets' cash and contracts and hierarchies' authority are rules about how individuals and groups work together (with rigorous discipline); how they communicate (widely and with granularity); and how leaders guide them toward a common goal (through example). Those rules, augmented by simple communication technologies and a lack of legal barriers to sharing information, create rich common knowledge, the ability to organize teams modularly, extraordinary motivation, and high levels of trust, which radically lowers transaction costs. Low transaction costs, in turn, make it profitable for organizations to perform more and smaller transactions--and so increase the pace and flexibility typical of high-performance organizations. Once the system achieves critical mass, it feeds on itself. The larger the system, the more broadly shared the knowledge, language, and work style. The greater individuals' reputational capital, the louder the applause and the stronger the motivation. The success of Linux is evidence of the power of that virtuous circle. Toyota's success is evidence that it is also powerful in conventional companies. PMID
Evans, Philip; Wolf, Bob
2005-01-01
Corporate leaders seeking to boost growth, learning, and innovation may find the answer in a surprising place: the Linux open-source software community. Linux is developed by an essentially volunteer, self-organizing community of thousands of programmers. Most leaders would sell their grandmothers for workforces that collaborate as efficiently, frictionlessly, and creatively as the self-styled Linux hackers. But Linux is software, and software is hardly a model for mainstream business. The authors have, nonetheless, found surprising parallels between the anarchistic, caffeinated, hirsute world of Linux hackers and the disciplined, tea-sipping, clean-cut world of Toyota engineering. Specifically, Toyota and Linux operate by rules that blend the self-organizing advantages of markets with the low transaction costs of hierarchies. In place of markets' cash and contracts and hierarchies' authority are rules about how individuals and groups work together (with rigorous discipline); how they communicate (widely and with granularity); and how leaders guide them toward a common goal (through example). Those rules, augmented by simple communication technologies and a lack of legal barriers to sharing information, create rich common knowledge, the ability to organize teams modularly, extraordinary motivation, and high levels of trust, which radically lowers transaction costs. Low transaction costs, in turn, make it profitable for organizations to perform more and smaller transactions--and so increase the pace and flexibility typical of high-performance organizations. Once the system achieves critical mass, it feeds on itself. The larger the system, the more broadly shared the knowledge, language, and work style. The greater individuals' reputational capital, the louder the applause and the stronger the motivation. The success of Linux is evidence of the power of that virtuous circle. Toyota's success is evidence that it is also powerful in conventional companies.
Scattering and; Delay, Scale, and Sum Migration
Lehman, S K
2011-07-06
How do we see? What is the mechanism? Consider standing in an open field on a clear sunny day. In the field are a yellow dog and a blue ball. From a wave-based remote sensing point of view the sun is a source of radiation. It is a broadband electromagnetic source which, for the purposes of this introduction, only the visible spectrum is considered (approximately 390 to 750 nanometers or 400 to 769 TeraHertz). The source emits an incident field into the known background environment which, for this example, is free space. The incident field propagates until it strikes an object or target, either the yellow dog or the blue ball. The interaction of the incident field with an object results in a scattered field. The scattered field arises from a mis-match between the background refractive index, considered to be unity, and the scattering object refractive index ('yellow' for the case of the dog, and 'blue' for the ball). This is also known as an impedance mis-match. The scattering objects are referred to as secondary sources of radiation, that radiation being the scattered field which propagates until it is measured by the two receivers known as 'eyes'. The eyes focus the measured scattered field to form images which are processed by the 'wetware' of the brain for detection, identification, and localization. When time series representations of the measured scattered field are available, the image forming focusing process can be mathematically modeled by delayed, scaled, and summed migration. This concept of optical propagation, scattering, and focusing have one-to-one equivalents in the acoustic realm. This document is intended to present the basic concepts of scalar scattering and migration used in wide band wave-based remote sensing and imaging. The terms beamforming and (delayed, scaled, and summed) migration are used interchangeably but are to be distinguished from the narrow band (frequency domain) beamforming to determine the direction of arrival of a signal, and
Sum over Histories Representation for Chemical Kinetics.
Bai, Shirong; Zhou, Dingyu; Davis, Michael J; Skodje, Rex T
2015-01-01
A new representation for chemical kinetics is introduced that is based on a sum over histories formulation that employs chemical pathways defined at a molecular level. The time evolution of a chemically reactive system is described by enumerating the most important pathways followed by a chemical moiety. An explicit formula for the pathway probabilities is derived and takes the form of an integral over a time-ordered product. When evaluating long pathways, the time-ordered product has a simple Monte Carlo representation that is computationally efficient. A small numerical stochastic simulation was used to identify the most important paths to include in the representation. The method was applied to a realistic H2/O2 combustion problem and is shown to yield accurate results. PMID:26263110
On the arithmetic sums of Cantor sets
NASA Astrophysics Data System (ADS)
Ilgar Eroglu, Kemal
2007-05-01
Let Cλ and Cγ be two affine Cantor sets in \\mathbb{R} with similarity dimensions dλ and dγ, respectively. We define an analogue of the Bandt-Graf condition for self-similar systems and use it to give necessary and sufficient conditions for having \\xyHa^{d_\\xyla+d_\\xyga}(C_\\xyla + C_\\xyga)>0 where Cλ + Cγ denotes the arithmetic sum of the sets. We use this result to analyse the orthogonal projection properties of sets of the form Cλ × Cγ. We prove that for Lebesgue almost all directions θ for which the projection is not one-to-one, the projection has zero (dλ + dγ)-dimensional Hausdorff measure. We demonstrate the results in the case when Cλ and Cγ are the middle-(1-2λ) and middle-(1-2γ) sets.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Theoretical Sum Frequency Generation Spectroscopy of Peptides
2015-01-01
Vibrational sum frequency generation (SFG) has become a very promising technique for the study of proteins at interfaces, and it has been applied to important systems such as anti-microbial peptides, ion channel proteins, and human islet amyloid polypeptide. Moreover, so-called “chiral” SFG techniques, which rely on polarization combinations that generate strong signals primarily for chiral molecules, have proven to be particularly discriminatory of protein secondary structure. In this work, we present a theoretical strategy for calculating protein amide I SFG spectra by combining line-shape theory with molecular dynamics simulations. We then apply this method to three model peptides, demonstrating the existence of a significant chiral SFG signal for peptides with chiral centers, and providing a framework for interpreting the results on the basis of the dependence of the SFG signal on the peptide orientation. We also examine the importance of dynamical and coupling effects. Finally, we suggest a simple method for determining a chromophore’s orientation relative to the surface using ratios of experimental heterodyne-detected signals with different polarizations, and test this method using theoretical spectra. PMID:25203677
Multireflection sum frequency generation vibrational spectroscopy.
Zhang, Chi; Jasensky, Joshua; Chen, Zhan
2015-08-18
We developed a multireflection data collection method in order to improve the signal-to-noise ratio (SNR) and sensitivity of sum frequency generation (SFG) spectroscopy, which we refer to as multireflection SFG, or MRSFG for short. To achieve MRSFG, a collinear laser beam propagation geometry was adopted and trapezoidal Dove prisms were used as sample substrates. An in-depth discussion on the signal and SNR in MRSFG was performed. We showed experimentally, with "m" total internal reflections in a Dove prism, MRSFG signal is ∼m times that of conventional SFG; SNR of the SFG signal-to-background is improved by a factor of >m(1/2) and
Iterated binomial sums and their associated iterated integrals
NASA Astrophysics Data System (ADS)
Ablinger, J.; Blümlein, J.; Raab, C. G.; Schneider, C.
2014-11-01
We consider finite iterated generalized harmonic sums weighted by the binomial binom{2k}{k} in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic, and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued alphabets. The values of the sums for N → ∞ and the iterated integrals at x = 1 lead to new constants, extending the set of special numbers given by the multiple zeta values, the cyclotomic zeta values and special constants which emerge in the limit N → ∞ of generalized harmonic sums. We develop algorithms to obtain the Mellin representations of these sums in a systematic way. They are of importance for the derivation of the asymptotic expansion of these sums and their analytic continuation to N in {C}. The associated convolution relations are derived for real parameters and can therefore be used in a wider context, as, e.g., for multi-scale processes. We also derive algorithms to transform iterated integrals over root-valued alphabets into binomial sums. Using generating functions we study a few aspects of infinite (inverse) binomial sums.
ERIC Educational Resources Information Center
Carraher, David W.; Earnest, Darrell
2003-01-01
We present classroom research on a variant of the guess-my-rule game, in which nine-year-old students make up linear functions and challenge classmates to determine their secret rule. We focus on issues students and their teacher confronted in inferring underlying rules and in deciding whether the conjectured rule matched the rule of the creators.…
College Sports: The Mystery of the Zero-Sum Game
ERIC Educational Resources Information Center
Getz, Malcolm; Siegfried, John J.
2012-01-01
In recent years, when a university may earn well over $10 million per year from fees for sports-broadcast rights, half of the teams still lose. Collegiate athletic competition is a zero sum game: The number of winners equals the number of losers. So why do universities spend growing sums of scarce resources on an activity when the odds of winning…
23 CFR 140.920 - Lump sum payments.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 23 Highways 1 2010-04-01 2010-04-01 false Lump sum payments. 140.920 Section 140.920 Highways FEDERAL HIGHWAY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION PAYMENT PROCEDURES REIMBURSEMENT Reimbursement for Railroad Work § 140.920 Lump sum payments. Where approved by FHWA, pursuant to 23 CFR...
23 CFR 140.920 - Lump sum payments.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 23 Highways 1 2014-04-01 2014-04-01 false Lump sum payments. 140.920 Section 140.920 Highways FEDERAL HIGHWAY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION PAYMENT PROCEDURES REIMBURSEMENT Reimbursement for Railroad Work § 140.920 Lump sum payments. Where approved by FHWA, pursuant to 23 CFR...
23 CFR 140.920 - Lump sum payments.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 23 Highways 1 2012-04-01 2012-04-01 false Lump sum payments. 140.920 Section 140.920 Highways FEDERAL HIGHWAY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION PAYMENT PROCEDURES REIMBURSEMENT Reimbursement for Railroad Work § 140.920 Lump sum payments. Where approved by FHWA, pursuant to 23 CFR...
23 CFR 140.920 - Lump sum payments.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 23 Highways 1 2011-04-01 2011-04-01 false Lump sum payments. 140.920 Section 140.920 Highways FEDERAL HIGHWAY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION PAYMENT PROCEDURES REIMBURSEMENT Reimbursement for Railroad Work § 140.920 Lump sum payments. Where approved by FHWA, pursuant to 23 CFR...
23 CFR 140.920 - Lump sum payments.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 23 Highways 1 2013-04-01 2013-04-01 false Lump sum payments. 140.920 Section 140.920 Highways FEDERAL HIGHWAY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION PAYMENT PROCEDURES REIMBURSEMENT Reimbursement for Railroad Work § 140.920 Lump sum payments. Where approved by FHWA, pursuant to 23 CFR...
Finding Sums for an Infinite Class of Alternating Series
ERIC Educational Resources Information Center
Chen, Zhibo; Wei, Sheng; Xiao, Xuerong
2012-01-01
Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…
Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms
Ablinger, Jakob; Schneider, Carsten; Blümlein, Johannes
2013-08-15
In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from ±1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincaré iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation with respect to the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.
Finding sums for an infinite class of alternating series
NASA Astrophysics Data System (ADS)
Chen, Zhibo; Wei, Sheng; Xiao, Xuerong
2012-07-01
Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the following form ?
An Electrophysiological Signature of Summed Similarity in Visual Working Memory
ERIC Educational Resources Information Center
van Vugt, Marieke K.; Sekuler, Robert; Wilson, Hugh R.; Kahana, Michael J.
2013-01-01
Summed-similarity models of short-term item recognition posit that participants base their judgments of an item's prior occurrence on that item's summed similarity to the ensemble of items on the remembered list. We examined the neural predictions of these models in 3 short-term recognition memory experiments using electrocorticographic/depth…
ERIC Educational Resources Information Center
Lim, Kim-Hui,; Har, Wai-Mun
2008-01-01
The lack of academic and thinking culture is getting more worried and becomes a major challenge to our academia society this 21st century. Few directions that move academia from "cogito ergo sum" to "consumo ergo sum" are actually leading us to "the end of academia". Those directions are: (1) the death of dialectic;…
Some rules for polydimensional squeezing
NASA Technical Reports Server (NTRS)
Manko, Vladimir I.
1994-01-01
The review of the following results is presented: For mixed state light of N-mode electromagnetic field described by Wigner function which has generic Gaussian form, the photon distribution function is obtained and expressed explicitly in terms of Hermite polynomials of 2N-variables. The momenta of this distribution are calculated and expressed as functions of matrix invariants of the dispersion matrix. The role of new uncertainty relation depending on photon state mixing parameter is elucidated. New sum rules for Hermite polynomials of several variables are found. The photon statistics of polymode even and odd coherent light and squeezed polymode Schroedinger cat light is given explicitly. Photon distribution for polymode squeezed number states expressed in terms of multivariable Hermite polynomials is discussed.
Trapezoidal rule quadrature algorithms for MIMD distributed memory computers
Lyness, J.N.; Plowman, S.E.
1994-08-01
An approach to multi-dimensional quadrature, designed to exploit parallel architectures, is described. This involves transforming the integral in such a way that an accurate result is given by the trapezoidal rule; and by evaluating the resulting sum in a manner which may be efficiently implemented on parallel architectures. This approach is to be implemented in the Liverpool NAG transputer library.
Zero-Sum Bias: Perceived Competition Despite Unlimited Resources
Meegan, Daniel V.
2010-01-01
Zero-sum bias describes intuitively judging a situation to be zero-sum (i.e., resources gained by one party are matched by corresponding losses to another party) when it is actually non-zero-sum. The experimental participants were students at a university where students’ grades are determined by how the quality of their work compares to a predetermined standard of quality rather than to the quality of the work produced by other students. This creates a non-zero-sum situation in which high grades are an unlimited resource. In three experiments, participants were shown the grade distribution after a majority of the students in a course had completed an assigned presentation, and asked to predict the grade of the next presenter. When many high grades had already been given, there was a corresponding increase in low grade predictions. This suggests a zero-sum bias, in which people perceive a competition for a limited resource despite unlimited resource availability. Interestingly, when many low grades had already been given, there was not a corresponding increase in high grade predictions. This suggests that a zero-sum heuristic is only applied in response to the allocation of desirable resources. A plausible explanation for the findings is that a zero-sum heuristic evolved as a cognitive adaptation to enable successful intra-group competition for limited resources. Implications for understanding inter-group interaction are also discussed. PMID:21833251
Generalized sums over histories for quantum gravity (II). Simplicial conifolds
NASA Astrophysics Data System (ADS)
Schleich, Kristin; Witt, Donald M.
1993-08-01
This paper examines the issues involved with concretely implementing a sum over conifolds in the formulation of euclidean sums over histories for gravity. The first step in precisely formulating any sum over topological spaces is that one must have an algorithmically implementable method of generating a list of all spaces in the set to be summed over. This requirement causes well known problems in the formulation of sums over manifolds in four or more dimensions; there is no algorithmic method of determining whether or not a topological space is an n-manifold in five or more dimensions and the issue of whether or not such an algorithm exists is open in four. However, as this paper shows, conifolds are algorithmically decidable in four dimensions. Thus the set of 4-conifolds provides a starting point for a concrete implementation of euclidean sums over histories in four dimensions. Explicit algorithms for summing over various sets of 4-conifolds are presented in the context of Regge calculus.
On the Adjacent Eccentric Distance Sum Index of Graphs
Qu, Hui; Cao, Shujuan
2015-01-01
For a given graph G, ε(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively. The adjacent eccentric distance sum index of a graph G is defined as ξsv(G)=∑v∈V(G)ε(v)D(v)deg(v), where D(v)=∑u∈V(G)d(u,v) is the sum of all distances from the vertex v. In this paper we derive some bounds for the adjacent eccentric distance sum index in terms of some graph parameters, such as independence number, covering number, vertex connectivity, chromatic number, diameter and some other graph topological indices. PMID:26091095
A Pascal-like triangle from finding power sums
NASA Astrophysics Data System (ADS)
Chen, Zhibo
2014-08-01
A Pascal-like triangle is constructed so that power sums can be conveniently obtained by college (or high school) students with no need for memorizing complicated formulas or performing difficult calculations.
Mental arithmetic activates analogic representations of internally generated sums.
Kallai, Arava Y; Schunn, Christian D; Fiez, Julie A
2012-08-01
The internal representation of numbers generated during calculation has received little attention. Much of the mathematics learning literature focuses on symbolic retrieval of math facts; in contrast, we critically test the hypothesis that internally generated numbers are represented analogically, using an approximate number system. In an fMRI study, the spontaneous processing of arithmetical expressions was tested. Participants passively viewed a sequence of double-digit addition expressions that summed to the same number. Adaptation was found in number-related regions in a fronto-parietal network. Following adaptation, arrays of dots were introduced, differing in their numerical distance from the sum of the addition expressions. Activation in voxels that showed adaptation to a repeated sum was also sensitive to the distance of the dot quantity from the sum. We conclude that participants exhibited adaptation to an internally generated number, that adapted representations were analogic in nature, and that these analogic representations may undergird arithmetic calculation. PMID:22732492
Standardization of 65Zn by sum-peak method.
Oliveira, E M; Iwahara, A; Poledna, R; Delgado, J U; da Silva, C J; da Silva, R L; Lopes, R T
2012-09-01
A commercial solution of (65)Zn was standardized by the sum peak-method using a planar HPGe detector. The activity results were compared with measurements made with a well type 4πγ ionization chamber, which is traceable to BIPM.RI (II)-K2.Zn-65 key-comparison performed in 2002. The sum-peak value was 42.79 kBq/g and the ionization chamber value was 42.74 kBq/g both at the reference date. The uncertainty obtained in the sum peak standardization was 0.25% (k=1), and in the ionization chamber was 0.85% (k=1). The results showed that sum-peak method can be used in (65)Zn standardization and this method is easier, simpler and more practical than others methods. PMID:22425414
Non-rigid summing of gated PET via optical flow
Klein, G.J.; Reutter, B.W.; Huesman, R.H. |
1996-12-31
A method for summing together datasets from gated cardiac PET acquisitions is described. Optical flow techniques are used to accurately model non-rigid motion present during the cardiac cycle so that a one-to-one mapping is found between each voxel of two gated volumes. Using this mapping, image summing can take place, producing a composite dataset with improved statistics and reduced motion-induced blur. Results using a data from a gated cardiac study on a dog are presented.
The odd-number sequence: squares and sums
NASA Astrophysics Data System (ADS)
Leyendekkers, J. V.; Shannon, A. G.
2015-11-01
Direct study of various characteristics of integers and their interactions is readily accessible to undergraduate students. Integers obviously fall in different classes of modular rings and thus have features unique to that class which can result in a variety of formations, particularly with sums of squares. The sum of the first n odd numbers is itself the square of n within the odd number sequence, from which testing for primality within the Fibonacci sequence is investigated in this note.
Phonological reduplication in sign language: Rules rule.
Berent, Iris; Dupuis, Amanda; Brentari, Diane
2014-01-01
Productivity-the hallmark of linguistic competence-is typically attributed to algebraic rules that support broad generalizations. Past research on spoken language has documented such generalizations in both adults and infants. But whether algebraic rules form part of the linguistic competence of signers remains unknown. To address this question, here we gauge the generalization afforded by American Sign Language (ASL). As a case study, we examine reduplication (X→XX)-a rule that, inter alia, generates ASL nouns from verbs. If signers encode this rule, then they should freely extend it to novel syllables, including ones with features that are unattested in ASL. And since reduplicated disyllables are preferred in ASL, such a rule should favor novel reduplicated signs. Novel reduplicated signs should thus be preferred to nonreduplicative controls (in rating), and consequently, such stimuli should also be harder to classify as nonsigns (in the lexical decision task). The results of four experiments support this prediction. These findings suggest that the phonological knowledge of signers includes powerful algebraic rules. The convergence between these conclusions and previous evidence for phonological rules in spoken language suggests that the architecture of the phonological mind is partly amodal.
Phonological reduplication in sign language: Rules rule
Berent, Iris; Dupuis, Amanda; Brentari, Diane
2014-01-01
Productivity—the hallmark of linguistic competence—is typically attributed to algebraic rules that support broad generalizations. Past research on spoken language has documented such generalizations in both adults and infants. But whether algebraic rules form part of the linguistic competence of signers remains unknown. To address this question, here we gauge the generalization afforded by American Sign Language (ASL). As a case study, we examine reduplication (X→XX)—a rule that, inter alia, generates ASL nouns from verbs. If signers encode this rule, then they should freely extend it to novel syllables, including ones with features that are unattested in ASL. And since reduplicated disyllables are preferred in ASL, such a rule should favor novel reduplicated signs. Novel reduplicated signs should thus be preferred to nonreduplicative controls (in rating), and consequently, such stimuli should also be harder to classify as nonsigns (in the lexical decision task). The results of four experiments support this prediction. These findings suggest that the phonological knowledge of signers includes powerful algebraic rules. The convergence between these conclusions and previous evidence for phonological rules in spoken language suggests that the architecture of the phonological mind is partly amodal. PMID:24959158
Modifying the sum over topological sectors and constraints on supergravity
NASA Astrophysics Data System (ADS)
Seiberg, Nathan
2010-07-01
The standard lore about the sum over topological sectors in quantum field theory is that locality and cluster decomposition uniquely determine the sum over such sectors, thus leading to the usual θ-vacua. We show that without changing the local degrees of freedom, a theory can be modified such that the sum over instantons should be restricted; e.g. one should include only instanton numbers which are divisible by some integer p. This conclusion about the configuration space of quantum field theory allows us to carefully reconsider the quantization of parameters in supergravity. In particular, we show that FI-terms and nontrivial Kähler forms are quantized. This analysis also leads to a new derivation of recent results about linearized supergravity.
ERIC Educational Resources Information Center
Dothan, Michael; Thompson, Fred
2009-01-01
Debt limits, interest coverage ratios, one-off balanced budget requirements, pay-as-you-go rules, and tax and expenditure limits are among the most important fiscal rules for constraining intertemporal transfers. There is considerable evidence that the least costly and most effective of such rules are those that focus directly on the rate of…
Rules on determining hearing appearances. Final rule.
2013-05-21
This final rule is another step in our continual efforts to handle workloads more effectively and efficiently. We are publishing final rules for portions of the rules we proposed in October 2007 that relate to persons, other than the claimant or any other party to the hearing, appearing by telephone. We are also clarifying that the administrative law judge (ALJ) will allow the claimant or any other party to a hearing to appear by telephone under certain circumstances when the claimant or other party requests to make his or her appearance in that manner. We expect that these final rules will make the hearings process more efficient and help us continue to reduce the hearings backlog. In addition, we made some minor editorial changes to our regulations that do not have any effect on the rights of claimants or any other parties.
Exploring the Sums of Powers of Consecutive q-Integers
ERIC Educational Resources Information Center
Kim, T.; Ryoo, C. S.; Jang, L. C.; Rim, S. H.
2005-01-01
The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…
Maneuver tracking using an adaptive Gaussian sum technique
NASA Astrophysics Data System (ADS)
Stubberud, Stephen C.; Kramer, Kathleen A.
2005-03-01
The best method to track through a maneuver is to know the motion model of the maneuvering target. Unfortunately, a priori knowledge of the maneuver is not usually known. If the motion model of the maneuver can be estimated quickly from the measurements then the resulting track estimate will be better than the a priori static model. An adaptive function approximation technique to improve the motion model while tracking is analyzed for its potential to track through various maneuvers. The basic function approximation technique is that of a Gaussian sum. The Gaussian sum approximates the function which represents the error between the initial static model and the actual model of the maneuver. The parameters of the Gaussian sum are identified on-line using a Kalman filter identification scheme. This scheme, used in conjunction with a Kalman filter tracker, creates a coupled technique that can improve the motion model quickly. This adaptive Gaussian sum approach to maneuver tracking has its performance analyzed for three maneuvers. These maneuvers include a maneuvering ballistic target, a target going through an s-curve, and real target with a multiple racetrack flight path. The results of these test cases demonstrate the capabilities of this approach to track maneuvering targets.
Note on permutation sum of color-ordered gluon amplitudes
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Feng, Bo; Fu, Chih-Hao
2012-01-01
In this Letter we show that under BCFW-deformation the large-z behavior of permutation sum of color-ordered gluon amplitudes found by Boels and Isermann in arxiv:arxiv:1109.5888 can be simply understood from the well known Kleiss-Kuijf relation and Bern-Carrasco-Johansson relation.
Two Different Approaches to Nonzero-Sum Stochastic Differential Games
Rainer, Catherine
2007-06-15
We make the link between two approaches to Nash equilibria for nonzero-sum stochastic differential games: the first one using backward stochastic differential equations and the second one using strategies with delay. We prove that, when both exist, the two notions of Nash equilibria coincide.
A Parametric Cumulative Sum Statistic for Person Fit
ERIC Educational Resources Information Center
Armstrong, Ronald D.; Shi, Min
2009-01-01
This article develops a new cumulative sum (CUSUM) statistic to detect aberrant item response behavior. Shifts in behavior are modeled with quadratic functions and a series of likelihood ratio tests are used to detect aberrancy. The new CUSUM statistic is compared against another CUSUM approach as well as traditional person-fit statistics. A…
A Solution to Weighted Sums of Squares as a Square
ERIC Educational Resources Information Center
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
For n = 1, 2, ... , we give a solution (x[subscript 1], ... , x[subscript n], N) to the Diophantine integer equation [image omitted]. Our solution has N of the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given n and given integer weights m[subscript…
The Sensitive Infrared Signal Detection by Sum Frequency Generation
NASA Technical Reports Server (NTRS)
Wong, Teh-Hwa; Yu, Jirong; Bai, Yingxin
2013-01-01
An up-conversion device that converts 2.05-micron light to 700 nm signal by sum frequency generation using a periodically poled lithium niobate crystal is demonstrated. The achieved 92% up-conversion efficiency paves the path to detect extremely weak 2.05-micron signal with well established silicon avalanche photodiode detector for sensitive lidar applications.
27 CFR 25.93 - Penal sum of bond.
Code of Federal Regulations, 2011 CFR
2011-04-01
... OF THE TREASURY LIQUORS BEER Bonds and Consents of Surety § 25.93 Penal sum of bond. (a)(1) Brewers... calculated at the rates prescribed by law which the brewer will become liable to pay during a calendar year during the period of the bond on beer: (i) Removed for transfer to the brewery from other breweries...
27 CFR 25.93 - Penal sum of bond.
Code of Federal Regulations, 2010 CFR
2010-04-01
... OF THE TREASURY LIQUORS BEER Bonds and Consents of Surety § 25.93 Penal sum of bond. (a)(1) Brewers... calculated at the rates prescribed by law which the brewer will become liable to pay during a calendar year during the period of the bond on beer: (i) Removed for transfer to the brewery from other breweries...
27 CFR 25.93 - Penal sum of bond.
Code of Federal Regulations, 2014 CFR
2014-04-01
... tax at the rates prescribed by law, on the maximum quantity of beer used in the production of... OF THE TREASURY ALCOHOL BEER Bonds and Consents of Surety § 25.93 Penal sum of bond. (a)(1) Brewers... calculated at the rates prescribed by law which the brewer will become liable to pay during a calendar...
27 CFR 25.93 - Penal sum of bond.
Code of Federal Regulations, 2012 CFR
2012-04-01
... OF THE TREASURY LIQUORS BEER Bonds and Consents of Surety § 25.93 Penal sum of bond. (a)(1) Brewers... calculated at the rates prescribed by law which the brewer will become liable to pay during a calendar year during the period of the bond on beer: (i) Removed for transfer to the brewery from other breweries...
27 CFR 25.93 - Penal sum of bond.
Code of Federal Regulations, 2013 CFR
2013-04-01
... tax at the rates prescribed by law, on the maximum quantity of beer used in the production of... OF THE TREASURY ALCOHOL BEER Bonds and Consents of Surety § 25.93 Penal sum of bond. (a)(1) Brewers... calculated at the rates prescribed by law which the brewer will become liable to pay during a calendar...
27 CFR 19.245 - Bonds and penal sums of bonds.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Bonds and penal sums of... Bonds and penal sums of bonds. The bonds, and the penal sums thereof, required by this subpart, are as follows: Penal Sum Type of bond Basis Minimum Maximum (a) Operations bond: (1) One plant bond—...
20 CFR 234.12 - 1937 Act lump-sum death payment.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 20 Employees' Benefits 1 2013-04-01 2012-04-01 true 1937 Act lump-sum death payment. 234.12 Section 234.12 Employees' Benefits RAILROAD RETIREMENT BOARD REGULATIONS UNDER THE RAILROAD RETIREMENT ACT LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.12 1937 Act lump-sum death payment. (a) The 1937...
20 CFR 234.12 - 1937 Act lump-sum death payment.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 20 Employees' Benefits 1 2014-04-01 2012-04-01 true 1937 Act lump-sum death payment. 234.12 Section 234.12 Employees' Benefits RAILROAD RETIREMENT BOARD REGULATIONS UNDER THE RAILROAD RETIREMENT ACT LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.12 1937 Act lump-sum death payment. (a) The 1937...
20 CFR 234.12 - 1937 Act lump-sum death payment.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 20 Employees' Benefits 1 2010-04-01 2010-04-01 false 1937 Act lump-sum death payment. 234.12 Section 234.12 Employees' Benefits RAILROAD RETIREMENT BOARD REGULATIONS UNDER THE RAILROAD RETIREMENT ACT LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.12 1937 Act lump-sum death payment. (a) The 1937...
20 CFR 234.12 - 1937 Act lump-sum death payment.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 20 Employees' Benefits 1 2012-04-01 2012-04-01 false 1937 Act lump-sum death payment. 234.12 Section 234.12 Employees' Benefits RAILROAD RETIREMENT BOARD REGULATIONS UNDER THE RAILROAD RETIREMENT ACT LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.12 1937 Act lump-sum death payment. (a) The 1937...
20 CFR 234.12 - 1937 Act lump-sum death payment.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 20 Employees' Benefits 1 2011-04-01 2011-04-01 false 1937 Act lump-sum death payment. 234.12 Section 234.12 Employees' Benefits RAILROAD RETIREMENT BOARD REGULATIONS UNDER THE RAILROAD RETIREMENT ACT LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.12 1937 Act lump-sum death payment. (a) The 1937...
Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
NASA Technical Reports Server (NTRS)
Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet
2015-01-01
When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating
Selection rules for the nonlinear interaction of internal gravity waves.
Jiang, Chung-Hsiang; Marcus, Philip S
2009-03-27
Two intersecting beams of internal gravity waves will generically create two wave packets by nonlinear interaction. The frequency of one packet will be the sum and that of the other packet will be the difference of the frequencies of the intersecting beams. In principle, each packet should form an "X" pattern, or "St. Andrew's cross" consisting of four beams outgoing from the point of intersection. Here we derive selection rules and show that most of the expected nonlinear beams are forbidden. These rules can also be applied to the reflection of a beam from a boundary.
29 CFR 4022.91 - When do these rules apply?
Code of Federal Regulations, 2010 CFR
2010-07-01
... we owe you because your plan owed them) at the time of your death, such as a payment of a lump-sum... to reimburse you for monthly underpayments. We may owe you benefits at the time of your death if— (1... any underpayment to you at the time of your death under the rule in § 4022.81(d)(2)(i) by paying it...
An efficient sampling technique for sums of bandpass functions
NASA Technical Reports Server (NTRS)
Lawton, W. M.
1982-01-01
A well known sampling theorem states that a bandlimited function can be completely determined by its values at a uniformly placed set of points whose density is at least twice the highest frequency component of the function (Nyquist rate). A less familiar but important sampling theorem states that a bandlimited narrowband function can be completely determined by its values at a properly chosen, nonuniformly placed set of points whose density is at least twice the passband width. This allows for efficient digital demodulation of narrowband signals, which are common in sonar, radar and radio interferometry, without the side effect of signal group delay from an analog demodulator. This theorem was extended by developing a technique which allows a finite sum of bandlimited narrowband functions to be determined by its values at a properly chosen, nonuniformly placed set of points whose density can be made arbitrarily close to the sum of the passband widths.
Sums of Hermitian Squares and the BMV Conjecture
NASA Astrophysics Data System (ADS)
Klep, Igor; Schweighofer, Markus
2008-11-01
We show that all the coefficients of the polynomial {tr}((A+tB)m)in{R}[t] are nonnegative whenever m≤13 is a nonnegative integer and A and B are positive semidefinite matrices of the same size. This has previously been known only for m≤7. The validity of the statement for arbitrary m has recently been shown to be equivalent to the Bessis-Moussa-Villani conjecture from theoretical physics. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.
Coincidence-Summing Corrections for Close Geometry Measurements
Gueray, R. Taygun
2008-11-11
For a given stellar temperature, nuclear reactions take place in the energy range of the Gamow window with the relatively low energies of the astrophysical interest for charged particle induced reactions. In order to measure the nuclear reaction cross sections with the activation method at projectile energies as low as possible, a gamma counting system that consists of Ge detectors and the irradiated target in close geometry is required. The presence of cascade transitions requires coincidence summing corrections that can not be ignored because of the very large solid angle. In this study, the determination of the summing correction factor and photopeak efficiency for a gamma spectrometer, as an example, composed of two Ge clover detectors in close geometry is briefly described.
Eisenhardt, K M; Sull, D N
2001-01-01
The success of Yahoo!, eBay, Enron, and other companies that have become adept at morphing to meet the demands of changing markets can't be explained using traditional thinking about competitive strategy. These companies have succeeded by pursuing constantly evolving strategies in market spaces that were considered unattractive according to traditional measures. In this article--the third in an HBR series by Kathleen Eisenhardt and Donald Sull on strategy in the new economy--the authors ask, what are the sources of competitive advantage in high-velocity markets? The secret, they say, is strategy as simple rules. The companies know that the greatest opportunities for competitive advantage lie in market confusion, but they recognize the need for a few crucial strategic processes and a few simple rules. In traditional strategy, advantage comes from exploiting resources or stable market positions. In strategy as simple rules, advantage comes from successfully seizing fleeting opportunities. Key strategic processes, such as product innovation, partnering, or spinout creation, place the company where the flow of opportunities is greatest. Simple rules then provide the guidelines within which managers can pursue such opportunities. Simple rules, which grow out of experience, fall into five broad categories: how- to rules, boundary conditions, priority rules, timing rules, and exit rules. Companies with simple-rules strategies must follow the rules religiously and avoid the temptation to change them too frequently. A consistent strategy helps managers sort through opportunities and gain short-term advantage by exploiting the attractive ones. In stable markets, managers rely on complicated strategies built on detailed predictions of the future. But when business is complicated, strategy should be simple. PMID:11189455
Baum, W M
1995-01-01
Behavior analysis risks intellectual isolation unless it integrates its explanations with evolutionary theory. Rule-governed behavior is an example of a topic that requires an evolutionary perspective for a full understanding. A rule may be defined as a verbal discriminative stimulus produced by the behavior of a speaker under the stimulus control of a long-term contingency between the behavior and fitness. As a discriminative stimulus, the rule strengthens listener behavior that is reinforced in the short run by socially mediated contingencies, but which also enters into the long-term contingency that enhances the listener's fitness. The long-term contingency constitutes the global context for the speaker's giving the rule. When a rule is said to be "internalized," the listener's behavior has switched from short- to long-term control. The fitness-enhancing consequences of long-term contingencies are health, resources, relationships, or reproduction. This view ties rules both to evolutionary theory and to culture. Stating a rule is a cultural practice. The practice strengthens, with short-term reinforcement, behavior that usually enhances fitness in the long run. The practice evolves because of its effect on fitness. The standard definition of a rule as a verbal statement that points to a contingency fails to distinguish between a rule and a bargain ("If you'll do X, then I'll do Y"), which signifies only a single short-term contingency that provides mutual reinforcement for speaker and listener. In contrast, the giving and following of a rule ("Dress warmly; it's cold outside") can be understood only by reference also to a contingency providing long-term enhancement of the listener's fitness or the fitness of the listener's genes. Such a perspective may change the way both behavior analysts and evolutionary biologists think about rule-governed behavior.
Signal replication by multiple sum- or difference-frequency generation.
McKinstrie, C J; Agarwal, A; Banwell, T C; Dailey, J M
2015-09-21
In this paper, the coupled-mode equations for sum-frequency generation (SFG) and difference-frequency generation (DFG) driven by multiple pumps are solved, and the noise figures of idler generation are determined. For SFG, the (common) noise figure is n, the number of pumps (and idlers), whereas for DFG, the (common) noise figure is 2, independent of n. Thus, DFG driven by multiple pumps enables the generation of multiple low-noise idlers.
Algebraic Riccati equations in zero-sum differential games
NASA Technical Reports Server (NTRS)
Johnson, T. L.; Chao, A.
1974-01-01
The procedure for finding the closed-loop Nash equilibrium solution of two-player zero-sum linear time-invariant differential games with quadratic performance criteria and classical information pattern may be reduced in most cases to the solution of an algebraic Riccati equation. Based on the results obtained by Willems, necessary and sufficient conditions for existence of solutions to these equations are derived, and explicit conditions for a scalar example are given.
Theory of sum frequency generation from metal surfaces
NASA Astrophysics Data System (ADS)
Liebsch, A.
The time-dependent density functional approach is used to evaluate the optical sum frequency generation from metal surfaces. Attention is focussed on the magnitude and frequency variation of the element χzzz(ω1,ω2). Four types of metal surfaces are considered: simple metals, alkali metal overlayers, noble metals, and charged metal surfaces. Differences and similarities with respect to second harmonic generation from these surfaces are pointed out.
Parafermionic derivation of Andrews-type multiple sums
NASA Astrophysics Data System (ADS)
Jacob, P.; Mathieu, P.
2005-09-01
A multi-parafermion basis of states for the {{\\bb Z}}_k parafermionic models is derived. Its generating function is constructed by elementary steps. It corresponds to the Andrews multiple sum which enumerates partitions whose parts separated by the distance k - 1 differ by at least 2. Two analogous bases are derived for graded parafermions; one of these entails a new expression for their fermionic characters.
Can nonhuman primates use tokens to represent and sum quantities?
Evans, Theodore A; Beran, Michael J; Addessi, Elsa
2010-11-01
It is unclear whether nonhuman animals can use physical tokens to flexibly represent various quantities by combining token values. Previous studies showed that chimpanzees (Pan troglodytes) and a macaque (Macaca mulatta) were only partly successful in tests involving sets of different-looking food containers representing different food quantities, while some capuchin monkeys (Cebus apella) have shown greater success in tests involving sets of various concrete objects representing different food quantities. Some of the discrepancy in results between these studies may be attributed to the different methods used. In an effort to reconcile these discrepancies, we presented two primates species, chimpanzees and capuchin monkeys, with two token tasks. The critical test in each task involved summing the value of multiple tokens of different types to make accurate quantity judgments. We found that, using either method, individuals of both species learned to associate individual tokens with specific quantities, as well as successfully compare individual tokens to one another or to sets of visible food items. However, regardless of method, only a few individuals exhibited the capacity to sum multiple tokens of different types and then use those summed values to make an optimal response. This suggests that flexible combination of symbolic stimuli in quantity judgments tasks is within the abilities of chimpanzees and capuchins but does not characterize the majority of individuals. Furthermore, the results suggest the need to carefully examine specific methodological details that may promote or hinder such possible representation. PMID:20836596
Mass Dependence of the Entropy Product and Sum
NASA Astrophysics Data System (ADS)
Zhang, Yuan; Gao, Sijie
2015-03-01
For black holes with multiple horizons, the area product of all horizons has been proven to be mass independent in many cases. Counterexamples were also found in some occasions. In this paper, we first prove a theorem derived from the first law of black hole thermodynamics and a mathematical lemma related to the Vandermonde determinant. With these arguments, we develop some general criteria for the mass independence of the entropy product as well as the entropy sum. In particular, if a d -dimensional spacetime is spherically symmetric and its radial metric function f (r ) is a Laurent series in r with the lowest power -m and the highest power n , we find the criterion is extremely simple: The entropy product is mass independent if and only if m ≥d -2 and n ≥4 -d . The entropy sum is mass independent if and only if m ≥d -2 and n ≥2 . Compared to previous works, our method does not require an exact expression of the metric. Our arguments turn out to be useful even for rotating black holes. By applying our theorem and lemma to a Myers-Perry black hole with spacetime dimension d , we show that the entropy product/sum is mass independent for all d >4 , while it is mass dependent only for d =4 , i.e., the Kerr solution.
Minimizing the Sum of Completion Times with Resource Dependant Times
NASA Astrophysics Data System (ADS)
Yedidsion, Liron; Shabtay, Dvir; Kaspi, Moshe
2008-10-01
We extend the classical minimization sum of completion times problem to the case where the processing times are controllable by allocating a nonrenewable resource. The quality of a solution is measured by two different criteria. The first criterion is the sum of completion times and the second is the total weighted resource consumption. We consider four different problem variations for treating the two criteria. We prove that this problem is NP-hard for three of the four variations even if all resource consumption weights are equal. However, somewhat surprisingly, the variation of minimizing the integrated objective function is solvable in polynomial time. Although the sum of completion times is arguably the most important scheduling criteria, the complexity of this problem, up to this paper, was an open question for three of the four variations. The results of this research have various implementations, including efficient battery usage on mobile devices such as mobile computer, phones and GPS devices in order to prolong their battery duration.
Can nonhuman primates use tokens to represent and sum quantities?
Evans, Theodore A; Beran, Michael J; Addessi, Elsa
2010-11-01
It is unclear whether nonhuman animals can use physical tokens to flexibly represent various quantities by combining token values. Previous studies showed that chimpanzees (Pan troglodytes) and a macaque (Macaca mulatta) were only partly successful in tests involving sets of different-looking food containers representing different food quantities, while some capuchin monkeys (Cebus apella) have shown greater success in tests involving sets of various concrete objects representing different food quantities. Some of the discrepancy in results between these studies may be attributed to the different methods used. In an effort to reconcile these discrepancies, we presented two primates species, chimpanzees and capuchin monkeys, with two token tasks. The critical test in each task involved summing the value of multiple tokens of different types to make accurate quantity judgments. We found that, using either method, individuals of both species learned to associate individual tokens with specific quantities, as well as successfully compare individual tokens to one another or to sets of visible food items. However, regardless of method, only a few individuals exhibited the capacity to sum multiple tokens of different types and then use those summed values to make an optimal response. This suggests that flexible combination of symbolic stimuli in quantity judgments tasks is within the abilities of chimpanzees and capuchins but does not characterize the majority of individuals. Furthermore, the results suggest the need to carefully examine specific methodological details that may promote or hinder such possible representation.
ERIC Educational Resources Information Center
Shea, Virginia
1994-01-01
Discusses rules of etiquette for communicating via computer networks, including conversing as politely as you would face-to-face; ethical behavior; becoming familiar with the domain that you are in; rules for discussion groups; quality of writing; sharing appropriate knowledge; and respecting individuals' privacy. (LRW)
ERIC Educational Resources Information Center
Murphy, David
2011-01-01
About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…
ERIC Educational Resources Information Center
Emo, Kenneth
2008-01-01
Rules guide and constrain participants' actions as they participate in any educational activity. This ethnographically driven case study examines how organizational rules--the implicit and explicit regulations that constrain actions and interactions--influence children to use science in the experiential educational activity of raising 4-H market…
Schmitt, David R.
2001-01-01
Although the elements of a fully stated rule (discriminative stimulus [SD], some behavior, and a consequence) can occur nearly contemporaneously with the statement of the rule, there is often a delay between the rule statement and the SD. The effects of this delay on rule following have not been studied in behavior analysis, but they have been investigated in rule-like settings in the areas of prospective memory (remembering to do something in the future) and goal pursuit. Discriminative events for some behavior can be event based (a specific setting stimulus) or time based. The latter are more demanding with respect to intention following and show age-related deficits. Studies suggest that the specificity with which the components of a rule (termed intention) are stated has a substantial effect on intention following, with more detailed specifications increasing following. Reminders of an intention, too, are most effective when they refer specifically to both the behavior and its occasion. Covert review and written notes are two effective strategies for remembering everyday intentions, but people who use notes appear not to be able to switch quickly to covert review. By focusing on aspects of the setting and rule structure, research on prospective memory and goal pursuit expands the agenda for a more complete explanation of rule effects. PMID:22478363
... 5-second rule" — that random saying about how food won't become contaminated with bacteria if you pick it up off the floor in 5 seconds or less. The 5-second rule has become such a part of our culture that scientists actually tested it. As you can ...
Katz, Anne
2016-05-01
I am getting better at following the rules as I grow older, although I still bristle at many of them. I was a typical rebellious teenager; no one understood me, David Bowie was my idol, and, one day, my generation was going to change the world. Now I really want people to understand me: David Bowie remains one of my favorite singers and, yes, my generation has changed the world, and not necessarily for the better. Growing up means that you have to make the rules, not just follow those set by others, and, at times, having rules makes a lot of sense. . PMID:27105186
Quantitative metrics of stove adoption using Stove Use Monitors (SUMs).
Ruiz-Mercado, Ilse; Canuz, Eduardo; Walker, Joan L; Smith, Kirk R
2013-10-01
The sustained use of cookstoves that are introduced to reduce fuel use or air pollution needs to be objectively monitored to verify the sustainability of these benefits. Quantifying stove adoption requires affordable tools, scalable methods and validated metrics of usage. We quantified the longitudinal patterns of chimney-stove use of 80 households in rural Guatemala, monitored with Stove Use Monitors (SUMs) during 32 months. We counted daily meals and days in use at each monitoring period and defined metrics like the percent stove-days in use (the fraction of days in use from all stoves and days monitored). Using robust Poisson regressions we detected small seasonal variations in stove usage, with peaks in the warm-dry season at 92% stove-days (95%CI: 87%,97%) and 2.56 average daily meals (95%CI: 2.40,2.74). With respect to these values, the percent stove-days in use decreased by 3% and 4% during the warm-rainy and cold-dry periods respectively, and the daily meals by 5% and 12% respectively. Cookstove age and household size at baseline did not affect usage. Qualitative indicators of use from recall questionnaires were consistent with SUMs measurements, indicating stable sustained use and questionnaire accuracy. These results reflect optimum conditions for cookstove adoption and for monitoring in this project, which may not occur in disseminations undertaken elsewhere. The SUMs measurements suggests that 90% stove-days is a more realistic best-case for sustained use than the 100% often assumed. Half of sample reported continued use of open-cookfires, highlighting the critical need to verify reduction of open-fire practices in stove disseminations.
Quantitative metrics of stove adoption using Stove Use Monitors (SUMs)
Ruiz-Mercado, Ilse; Canuz, Eduardo; Walker, Joan L.; Smith, Kirk R.
2014-01-01
The sustained use of cookstoves that are introduced to reduce fuel use or air pollution needs to be objectively monitored to verify the sustainability of these benefits. Quantifying stove adoption requires affordable tools, scalable methods and validated metrics of usage. We quantified the longitudinal patterns of chimney-stove use of 80 households in rural Guatemala, monitored with Stove Use Monitors (SUMs) during 32 months. We counted daily meals and days in use at each monitoring period and defined metrics like the percent stove-days in use (the fraction of days in use from all stoves and days monitored). Using robust Poisson regressions we detected small seasonal variations in stove usage, with peaks in the warm-dry season at 92% stove-days (95%CI: 87%,97%) and 2.56 average daily meals (95%CI: 2.40,2.74). With respect to these values, the percent stove-days in use decreased by 3% and 4% during the warm-rainy and cold-dry periods respectively, and the daily meals by 5% and 12% respectively. Cookstove age and household size at baseline did not affect usage. Qualitative indicators of use from recall questionnaires were consistent with SUMs measurements, indicating stable sustained use and questionnaire accuracy. These results reflect optimum conditions for cookstove adoption and for monitoring in this project, which may not occur in disseminations undertaken elsewhere. The SUMs measurements suggests that 90% stove-days is a more realistic best-case for sustained use than the 100% often assumed. Half of sample reported continued use of open-cookfires, highlighting the critical need to verify reduction of open-fire practices in stove disseminations. PMID:25258474
Screening and Spectral Summing of LANL Empty Waste Drums - 13226
Gruetzmacher, Kathleen M.; Bustos, Roland M.; Ferran, Scott G.; Gallegos, Lucas E.; Lucero, Randy P.
2013-07-01
Empty 55-gallon drums that formerly held transuranic (TRU) waste (often over-packed in 85- gallon drums) are generated at LANL and require radiological characterization for disposition. These drums are typically measured and analyzed individually using high purity germanium (HPGe) gamma detectors. This approach can be resource and time intensive. For a project requiring several hundred drums to be characterized in a short time frame, an alternative approach was developed. The approach utilizes a combination of field screening and spectral summing that was required to be technically defensible and meet the Nevada Nuclear Security Site (NNSS) Waste Acceptance Criteria (WAC). In the screening phase of the operation, the drums were counted for 300 seconds (compared to 600 seconds for the typical approach) and checked against Low Level (LL)/TRU thresholds established for each drum configuration and detector. Multiple TRU nuclides and multiple gamma rays for each nuclide were evaluated using an automated spreadsheet utility that can process data from up to 42 drums at a time. Screening results were reviewed by an expert analyst to confirm the field LL/TRU determination. The spectral summing analysis technique combines spectral data (channel-by-channel) associated with a group of individual waste containers producing a composite spectrum. The grouped drums must meet specific similarity criteria. Another automated spreadsheet utility was used to spectral sum data from an unlimited number of similar drums grouped together. The composite spectrum represents a virtual combined drum for the group of drums and was analyzed using the SNAP{sup TM}/Radioassay Data Sheet (RDS)/Batch Data Report (BDR) method. The activity results for a composite virtual drum were divided equally amongst the individual drums to generate characterization results for each individual drum in the group. An initial batch of approximately 500 drums were measured and analyzed in less than 2 months in 2011
A new method for taming tensor sum-integrals
NASA Astrophysics Data System (ADS)
Ghisoiu, Ioan; Schröder, York
2012-11-01
We report on the computation of a class of massless bosonic three-loop vacuum sum-integrals which are key building blocks for an evaluation of the Debye screening mass in hot QCD. Generalizing known techniques and introducing the concept of tensor reduction by dimensionality shifts (known to the zero-temperature community since the work of Tarasov in 1996) to finite temperature, we are able to treat hitherto unaccessible cases, which will allow us to finalize the long-term project of NNLO Debye mass evaluation.
Comparison between parallel transfer matrix method and admittance sum method.
Verdière, Kévin; Panneton, Raymond; Elkoun, Saïd; Dupont, Thomas; Leclaire, Philippe
2014-08-01
A transfer matrix method to predict absorption coefficient and transmission loss of parallel assemblies of materials which can be expressed by a 2 × 2 transfer matrix was published recently. However, the usual method based on the sum of admittances is largely used to predict also surface admittance of parallel assemblies. This paper aims to highlight differences between both methods through three examples on a parallel assembly backed by (1) a rigid wall, (2) an air cavity, and (3) an anechoic termination.
NASA Astrophysics Data System (ADS)
Zielinski, Sarah
2006-04-01
The U.S. Environmental Protection Agency (EPA) and the U.S. Army Corps of Engineers released on 28 March a draft of a new rule to guide compensatory mitigation for when wetlands are unavoidably lost due to development. However, whether the rule is successful in preventing a net loss in wetlands will depend largely on its implementation, according to two wetlands scientists who evaluated the issue for the U.S. National Research Council (NRC) in 2001. Under the federal Clean Water Act, developers who seek to build on wetlands must compensate for any wetlands loss if they are unable to avoid or minimize the loss. Such compensation is covered under the newly proposed compensatory mitigation rule. Benjamin Grumbles, EPA assistant administrator for water, called the rule an ``innovative new standard that will accelerate the pace of wetlands conservation and restoration.''
... works with other insurance Find health & drug plans Drug plan coverage rules Note Call your Medicare drug ... shingles vaccine) when medically necessary to prevent illness. Drugs you get in hospital outpatient settings In most ...
(FIELD) SYMMETRIZATION SELECTION RULES
P. PAGE
2000-08-01
QCD and QED exhibit an infinite set of three-point Green's functions that contain only OZI rule violating contributions, and (for QCD) are subleading in the large N{sub c} expansion. We prove that the QCD amplitude for a neutral hybrid {l_brace}1,3,5. . .{r_brace}{+-} exotic current to create {eta}{pi}{sup 0} only comes from OZI rule violating contributions under certain conditions, and is subleading in N{sub c}.
Pushing the rules: effects and aftereffects of deliberate rule violations.
Wirth, Robert; Pfister, Roland; Foerster, Anna; Huestegge, Lynn; Kunde, Wilfried
2016-09-01
Most of our daily life is organized around rules and social norms. But what makes rules so special? And what if one were to break a rule intentionally? Can we simply free us from the present set of rules or do we automatically adhere to them? How do rule violations influence subsequent behavior? To investigate the effects and aftereffects of violating simple S-R rule, we conducted three experiments that investigated continuous finger-tracking responses on an iPad. Our experiments show that rule violations are distinct from rule-based actions in both response times and movement trajectories, they take longer to initiate and execute, and their movement trajectory is heavily contorted. Data not only show differences between the two types of response (rule-based vs. violation), but also yielded a characteristic pattern of aftereffects in case of rule violations: rule violations do not trigger adaptation effects that render further rule violations less difficult, but every rule violation poses repeated effort on the agent. The study represents a first step towards understanding the signature and underlying mechanisms of deliberate rule violations, they cannot be acted out by themselves, but require the activation of the original rule first. Consequently, they are best understood as reformulations of existing rules that are not accessible on their own, but need to be constantly derived from the original rule, with an add-on that might entail an active tendency to steer away from mental representations that reflect (socially) unwanted behavior.
Stability of Zero-Sum Games in Evolutionary Game Theory
NASA Astrophysics Data System (ADS)
Knebel, Johannes; Krueger, Torben; Weber, Markus F.; Frey, Erwin
2014-03-01
Evolutionary game theory has evolved into a successful theoretical concept to study mechanisms that govern the evolution of ecological communities. On a mathematical level, this theory was formalized in the framework of the celebrated replicator equations (REs) and its stochastic generalizations. In our work, we analyze the long-time behavior of the REs for zero-sum games with arbitrarily many strategies, which are generalized versions of the children's game Rock-Paper-Scissors.[1] We demonstrate how to determine the strategies that survive and those that become extinct in the long run. Our results show that extinction of strategies is exponentially fast in generic setups, and that conditions for the survival can be formulated in terms of the Pfaffian of the REs' antisymmetric payoff matrix. Consequences for the stochastic dynamics, which arise in finite populations, are reflected by a generalized scaling law for the extinction time in the vicinity of critical reaction rates. Our findings underline the relevance of zero-sum games as a reference for the analysis of other models in evolutionary game theory.
Sum-Frequency Generation from Chiral Media and Interfaces
Ji, Na
2006-02-13
Sum frequency generation (SFG), a second-order nonlinear optical process, is electric-dipole forbidden in systems with inversion symmetry. As a result, it has been used to study chiral media and interfaces, systems intrinsically lacking inversion symmetry. This thesis describes recent progresses in the applications of and new insights into SFG from chiral media and interfaces. SFG from solutions of chiral amino acids is investigated, and a theoretical model explaining the origin and the strength of the chiral signal in electronic-resonance SFG spectroscopy is discussed. An interference scheme that allows us to distinguish enantiomers by measuring both the magnitude and the phase of the chiral SFG response is described, as well as a chiral SFG microscope producing chirality-sensitive images with sub-micron resolution. Exploiting atomic and molecular parity nonconservation, the SFG process is also used to solve the Ozma problems. Sum frequency vibrational spectroscopy is used to obtain the adsorption behavior of leucine molecules at air-water interfaces. With poly(tetrafluoroethylene) as a model system, we extend the application of this surface-sensitive vibrational spectroscopy to fluorine-containing polymers.
NASA Astrophysics Data System (ADS)
Carstens, C. J.
2015-04-01
Randomization of binary matrices has become one of the most important quantitative tools in modern computational biology. The equivalent problem of generating random directed networks with fixed degree sequences has also attracted a lot of attention. However, it is very challenging to generate truly unbiased random matrices with fixed row and column sums. Strona et al. [Nat. Commun. 5, 4114 (2014), 10.1038/ncomms5114] introduce the innovative Curveball algorithm and give numerical support for the proposition that it generates truly random matrices. In this paper, we present a rigorous proof of convergence to the uniform distribution. Furthermore, we show the Curveball algorithm must include certain failed trades to ensure uniform sampling.
20 CFR 234.11 - 1974 Act lump-sum death payment.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 20 Employees' Benefits 1 2011-04-01 2011-04-01 false 1974 Act lump-sum death payment. 234.11... LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.11 1974 Act lump-sum death payment. (a) The total amount... household” as the employee at the time of the employee's death. (Refer to § 234.21 for an explanation...
20 CFR 234.11 - 1974 Act lump-sum death payment.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 20 Employees' Benefits 1 2014-04-01 2012-04-01 true 1974 Act lump-sum death payment. 234.11... LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.11 1974 Act lump-sum death payment. (a) The total amount... household” as the employee at the time of the employee's death. (Refer to § 234.21 for an explanation...
20 CFR 234.11 - 1974 Act lump-sum death payment.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 20 Employees' Benefits 1 2013-04-01 2012-04-01 true 1974 Act lump-sum death payment. 234.11... LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.11 1974 Act lump-sum death payment. (a) The total amount... household” as the employee at the time of the employee's death. (Refer to § 234.21 for an explanation...
20 CFR 234.11 - 1974 Act lump-sum death payment.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 20 Employees' Benefits 1 2010-04-01 2010-04-01 false 1974 Act lump-sum death payment. 234.11... LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.11 1974 Act lump-sum death payment. (a) The total amount... household” as the employee at the time of the employee's death. (Refer to § 234.21 for an explanation...
20 CFR 234.11 - 1974 Act lump-sum death payment.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 20 Employees' Benefits 1 2012-04-01 2012-04-01 false 1974 Act lump-sum death payment. 234.11... LUMP-SUM PAYMENTS Lump-Sum Death Payment § 234.11 1974 Act lump-sum death payment. (a) The total amount... household” as the employee at the time of the employee's death. (Refer to § 234.21 for an explanation...
Updating Best Practices: Applying On-Screen Reading Strategies to Résumé Writing
ERIC Educational Resources Information Center
Diaz, Charlsye Smith
2013-01-01
The best practices presented in textbooks and professional publications provide separate guidelines for paper-based and electronic or "scannable" résumés. This article recommends changing these practices so that writers can prepare one résumé for both paper and electronic delivery. These recommendations focus on three areas. Résumés…
An Alternate Approach to Alternating Sums: A Method to DIE for
ERIC Educational Resources Information Center
Benjamin, Arthur T.; Quinn, Jennifer J.
2008-01-01
Positive sums count. Alternating sums match. Alternating sums of binomial coefficients, Fibonacci numbers, and other combinatorial quantities are analyzed using sign-reversing involutions. In particular, we describe the quantity being considered, match positive and negative terms through an Involution, and count the Exceptions to the matching rule…
29 CFR 778.310 - Fixed sum for varying amounts of overtime.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 29 Labor 3 2012-07-01 2012-07-01 false Fixed sum for varying amounts of overtime. 778.310 Section... Special Problems Lump Sum Attributed to Overtime § 778.310 Fixed sum for varying amounts of overtime. A... employee a fixed salary regardless of the number of hours worked in excess of the applicable maximum...
29 CFR 778.310 - Fixed sum for varying amounts of overtime.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 29 Labor 3 2013-07-01 2013-07-01 false Fixed sum for varying amounts of overtime. 778.310 Section... Special Problems Lump Sum Attributed to Overtime § 778.310 Fixed sum for varying amounts of overtime. A... employee a fixed salary regardless of the number of hours worked in excess of the applicable maximum...
29 CFR 778.309 - Fixed sum for constant amount of overtime.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 29 Labor 3 2013-07-01 2013-07-01 false Fixed sum for constant amount of overtime. 778.309 Section... Special Problems Lump Sum Attributed to Overtime § 778.309 Fixed sum for constant amount of overtime. Where an employee works a regular fixed number of hours in excess of the statutory maximum each...
29 CFR 778.309 - Fixed sum for constant amount of overtime.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 29 Labor 3 2012-07-01 2012-07-01 false Fixed sum for constant amount of overtime. 778.309 Section... Special Problems Lump Sum Attributed to Overtime § 778.309 Fixed sum for constant amount of overtime. Where an employee works a regular fixed number of hours in excess of the statutory maximum each...
The Last and Weiss Rorschach Sum E in a normal sample.
Greenwald, D F
1990-06-01
For 62 undergraduate women correlations of Rorschach Sum E with scores on 16 PF, Barron's MMPI Ego Strength Scale, the Eagly Self-esteem Scale, Kaplan's Self-derogation Scale, and MAACL. Anxiety, depression, and hostility showed FC+ was the only Sum E component associated with adaptive functioning and so Sum E is of limited usefulness. PMID:2377423
Westgard, J O; Groth, T; Aronsson, T; Falk, H; de Verdier, C H
1977-10-01
When assessing the performance of an internal quality control system, it is useful to determine the probability for false rejections (pfr) and the probability for error detection (ped). These performance characteristics are estimated here by use of a computer stimulation procedure. The control rules studied include those commonly employed with Shewhart-type control charts, a cumulative sum rule, and rules applicable when a series of control measurements are treated as a single control observation. The error situations studied include an increase in random error, a systematic shift, a systematic drift, and mixtures of these. The probability for error detection is very dependent on the number of control observations and the choice of control rules. No one rule is best for detecting all errors, thus combinations of rules are desirable. Some appropriate combinations are suggested and their performance characteristics are presented.
Yan, Xinhu; Chen, Jian-Ping; Choi, Seonho; Lu, Hai-Jiang; Meziani, Zein-Eddine; Oh, Yoomin; Sulkosky, Vince; Ye, Yunxiu; Yao, Huan
2011-05-01
A precision measurment of inclusive electron scattering cross sections is carried out at Jefferson Lab in the quasi-elastic region for ^{4}He, ^{12}C, ^{56}Fe and ^{208}Pb targets. The longitudinal (R_{L}) and transverse (R_{T}) response functions of the nucleon need to be extracted precisely in the momentum transfer range 0.55 GeV/c ≤ |q| ≤ 1.0 GeV/c. To achieve the above goal, a NaI (Tl) calorimeter is used to distinguish good electrons from background, including pions and low energy electrons rescattered from the walls of the spectrometer magnets. Due to a large set of kinematics and changes in HV settings, a number of calibrations are performed for the NaI (Tl) detector. Corrections for a few blocks of NaI (Tl) with bad or no signal are applied. The resolution of the NaI (Tl) detector after calibration reached ɤE/√E ≈ 3% at E = 1 GeV. The performance of the NaI (Tl) detector is compared with a simulation.
New Test of the Friedmann-Lemaître-Robertson-Walker Metric Using the Distance Sum Rule.
Räsänen, Syksy; Bolejko, Krzysztof; Finoguenov, Alexis
2015-09-01
We present a new test of the validity of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, based on comparing the distance from redshift 0 to z(1) and from z(1) to z(2) to the distance from 0 to z(2). If the Universe is described by the FLRW metric, the comparison provides a model-independent measurement of spatial curvature. The test relies on geometrical optics, it is independent of the matter content of the Universe and the applicability of the Einstein equation on cosmological scales. We apply the test to observations, using the Union2.1 compilation of supernova distances and Sloan Lens ACS Survey galaxy strong lensing data. The FLRW metric is consistent with the data, and the spatial curvature parameter is constrained to be -1.22<Ω(K0)<0.63, or -0.08<Ω(K0)<0.97 with a prior from the cosmic microwave background and the local Hubble constant, though modeling of the lenses is a source of significant systematic uncertainty. PMID:26382671
SEU System Analysis: Not Just the Sum of All Parts
NASA Technical Reports Server (NTRS)
Berg, Melanie D.; Label, Kenneth
2014-01-01
Single event upset (SEU) analysis of complex systems is challenging. Currently, system SEU analysis is performed by component level partitioning and then either: the most dominant SEU cross-sections (SEUs) are used in system error rate calculations; or the partition SEUs are summed to eventually obtain a system error rate. In many cases, system error rates are overestimated because these methods generally overlook system level derating factors. The problem with overestimating is that it can cause overdesign and consequently negatively affect the following: cost, schedule, functionality, and validation/verification. The scope of this presentation is to discuss the risks involved with our current scheme of SEU analysis for complex systems; and to provide alternative methods for improvement.
Sum Frequency Generation Studies of Hydrogenation Reactions on Platinum Nanoparticles
Krier, James M.
2013-08-31
Sum Frequency Generation (SFG) vibrational spectroscopy is used to characterize intermediate species of hydrogenation reactions on the surface of platinum nanoparticle catalysts. In contrast to other spectroscopy techniques which operate in ultra-high vacuum or probe surface species after reaction, SFG collects information under normal conditions as the reaction is taking place. Several systems have been studied previously using SFG on single crystals, notably alkene hydrogenation on Pt(111). In this thesis, many aspects of SFG experiments on colloidal nanoparticles are explored for the first time. To address spectral interference by the capping agent (PVP), three procedures are proposed: UV cleaning, H2 induced disordering and calcination (core-shell nanoparticles). UV cleaning and calcination physically destroy organic capping while disordering reduces SFG signal through a reversible structural change by PVP.
Sparse Zero-Sum Games as Stable Functional Feature Selection
Sokolovska, Nataliya; Teytaud, Olivier; Rizkalla, Salwa; Clément, Karine; Zucker, Jean-Daniel
2015-01-01
In large-scale systems biology applications, features are structured in hidden functional categories whose predictive power is identical. Feature selection, therefore, can lead not only to a problem with a reduced dimensionality, but also reveal some knowledge on functional classes of variables. In this contribution, we propose a framework based on a sparse zero-sum game which performs a stable functional feature selection. In particular, the approach is based on feature subsets ranking by a thresholding stochastic bandit. We provide a theoretical analysis of the introduced algorithm. We illustrate by experiments on both synthetic and real complex data that the proposed method is competitive from the predictive and stability viewpoints. PMID:26325268
Sparse Zero-Sum Games as Stable Functional Feature Selection.
Sokolovska, Nataliya; Teytaud, Olivier; Rizkalla, Salwa; Clément, Karine; Zucker, Jean-Daniel
2015-01-01
In large-scale systems biology applications, features are structured in hidden functional categories whose predictive power is identical. Feature selection, therefore, can lead not only to a problem with a reduced dimensionality, but also reveal some knowledge on functional classes of variables. In this contribution, we propose a framework based on a sparse zero-sum game which performs a stable functional feature selection. In particular, the approach is based on feature subsets ranking by a thresholding stochastic bandit. We provide a theoretical analysis of the introduced algorithm. We illustrate by experiments on both synthetic and real complex data that the proposed method is competitive from the predictive and stability viewpoints. PMID:26325268
Summing up all genus free energy of ABJM matrix model
NASA Astrophysics Data System (ADS)
Fuji, Hiroyuki; Hirano, Shinji; Moriyama, Sanefumi
2011-08-01
The localization technique allows us to compute the free energy of the U( N) k × U( N)- k Chern-Simons-matter theory dual to type IIA strings on AdS 4 × CP 3 from weak to strong 't Hooft coupling λ = N/ k at finite N, as demonstrated by Drukker, Mariño, and Putrov. In this note we study further the free energy at large 't Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up allthe1/ N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form — the Airy function, {text{Ai}}left( {{{left( {{{{π {k^2}}} left/ {{sqrt {2} }} right.}} right)}^{{{2} left/ {3} right.}}}{λ_{text{ren}}}} right) , with the renormalized 't Hooft coupling λren.
Structure of supersymmetric sums in multiloop unitarity cuts
Bern, Z.; Carrasco, J. J. M.; Ita, H.; Johansson, H.; Roiban, R.
2009-09-15
In this paper we describe algebraic and diagrammatic methods related to the maximally helicity-violating generating function method for evaluating and exposing the structure of supersymmetric sums over the states crossing generalized unitarity cuts of multiloop amplitudes in four dimensions. We focus mainly on cuts of maximally supersymmetric Yang-Mills amplitudes. We provide various concrete examples, some of which are directly relevant for the calculation of four-loop amplitudes. Additionally, we discuss some cases with less-than-maximal supersymmetry. The results of these constructions carry over to generalized cuts of multiloop supergravity amplitudes through use of the Kawai-Lewellen-Tye relations between gravity and gauge-theory tree amplitudes.
Juric, R.
1996-12-31
Any methodology for information systems development defines rules and conditions that are to be followed and satisfied when applying it to developing analysis and design models of a system. The newest attempt to achieve a successful systems development and establish standards in object oriented analysis and design technologies resulted in the unified method documentation set, version 0.8 being published in late 1995. In this paper I will analyse the first draft and present a set of rules that must be satisfied by the valid unified method. The rules are divided into different sections: (A) classes/objects and categories, (B) attributes and operations, (C) associations and inheritance, (D) message trace diagram/object message diagram/state diagram/use cases.
Residue theorem and summing over Kaluza-Klein excitations
Feng Taifu; Chen Jianbin; Gao Tiejun; Sun Kesheng
2011-11-01
Applying the equations of motion together with corresponding boundary conditions of bulk profiles at infrared and ultraviolet branes, we verify some lemmas on the eigenvalues of Kaluza-Klein modes in extension of the standard model with a warped extra dimension and the custodial symmetry SU(3){sub c}xSU(2){sub L}xSU(2){sub R}xU(1){sub X}xP{sub LR}. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluza-Klein excitations and sum over the series through the residue theorem. The method can also be applied to sum over the infinite series of Kaluza-Klein excitations in a universal extra dimension. Furthermore, we analyze the possible connection between the propagators in five-dimensional full theory and the product of bulk profiles with corresponding propagators of exciting Kaluza-Klein modes in four-dimensional effective theory, and recover some relations presented in the literature for warped and universal extra dimensions, respectively. As an example, we present the correction from new physics to the branching ratio of B{yields}X{sub s{gamma}} to the order O({mu}{sub EW}{sup 2}/{Lambda}{sub KK}{sup 2}) in extension of the standard model with a warped extra dimension and the custodial symmetry, where {Lambda}{sub KK} denotes the energy scale of low-lying Kaluza-Klein excitations and {mu}{sub EW} denotes the electroweak energy scale.
Novice Rules for Projectile Motion.
ERIC Educational Resources Information Center
Maloney, David P.
1988-01-01
Investigates several aspects of undergraduate students' rules for projectile motion including general patterns; rules for questions about time, distance, solids and liquids; and changes in rules when asked to ignore air resistance. Reports approach differences by sex and high school physics experience, and that novice rules are situation…
NASA Astrophysics Data System (ADS)
Cioslowski, Jerzy; Liu, Guanghua; Mosquera Castro, Ricardo A.
2000-12-01
Numerical experiments demonstrate that the accuracy of stretching force constants ke provided by Badger's rule is unlikely to be substantially improved either by modification of the functional dependence on the equilibrium bond length Re or the inclusion of bond parameters related to electron density. These results, based upon both the experimental and QCISD/6-311++G(3d2f, 3p2d) values of Re and ke, imply that most of the universal characteristics of the bond strength vs. bond length dependence are accounted for by Badger's rule, the more detailed features being unexplainable by first-order response properties such as electron density.
2016-03-01
The Department of Veterans Affairs (VA) adopts as final an interim final rule that amends its medical regulation that governs Vet Center services. The National Defense Authorization Act for Fiscal Year 2013 (the 2013 Act) requires Vet Centers to provide readjustment counseling services to broader groups of veterans, members of the Armed Forces, including a member of a reserve component of the Armed Forces, and family members of such veterans and members. This final rule adopts as final the regulatory criteria to conform to the 2013 Act, to include new and revised definitions. PMID:26934755
Cutkosky rules for superstring field theory
NASA Astrophysics Data System (ADS)
Pius, Roji; Sen, Ashoke
2016-10-01
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2005-01-01
In 1750, the Swiss mathematician Gabriel Cramer published a well-written algebra book entitled "Introduction a l'Analyse des Lignes Courbes Algebriques." In the appendix to this book, Cramer gave, without proof, the rule named after him for solving a linear system of equations using determinants (Kosinki, 2001). Since then several derivations of…
ERIC Educational Resources Information Center
Karp, Karen S.; Bush, Sarah B.; Dougherty, Barbara J.
2014-01-01
Overgeneralizing commonly accepted strategies, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students' math careers. In this article, the authors present thirteen pervasive mathematics rules that "expire." With the…
NASA Technical Reports Server (NTRS)
Weaver, E R; Pickering, S F
1924-01-01
This report prepared for the National Advisory Committee for Aeronautics, describes an airship slide rule developed by the Gas-Chemistry Section of the Bureau of Standards, at the request of the Bureau of Engineering of the Navy Department. It is intended primarily to give rapid solutions of a few problems of frequent occurrence in airship navigation, but it can be used to advantage in solving a great variety of problems, involving volumes, lifting powers, temperatures, pressures, altitudes and the purity of the balloon gas. The rule is graduated to read directly in the units actually used in making observations, constants and conversion factors being taken care of by the length and location of the scales. It is thought that with this rule practically any problem likely to arise in this class of work can be readily solved after the user has become familiar with the operation of the rule; and that the solution will, in most cases, be as accurate as the data warrant.
Crispen's Five Antivirus Rules.
ERIC Educational Resources Information Center
Crispen, Patrick Douglas
2000-01-01
Explains five rules to protect computers from viruses. Highlights include commercial antivirus software programs and the need to upgrade them periodically (every year to 18 months); updating virus definitions at least weekly; scanning attached files from email with antivirus software before opening them; Microsoft Word macro protection; and the…
Crispen's Five Antivirus Rules.
ERIC Educational Resources Information Center
Crispen, Patrick Douglas
2000-01-01
Provides rules for protecting computers from viruses, Trojan horses, or worms. Topics include purchasing commercial antivirus programs and keeping them updated; updating virus definitions weekly; precautions before opening attached files; macro virus protection in Microsoft Word; and precautions with executable files. (LRW)
ERIC Educational Resources Information Center
Benabou, Roland; Tirole, Jean
2004-01-01
We develop a theory of internal commitments or "personal rules" based on self-reputation over one's willpower, which transforms lapses into precedents that undermine future self-restraint. The foundation for this mechanism is the imperfect recall of past motives and feelings, leading people to draw inferences from their past actions. The degree of…
Tree Branching: Leonardo da Vinci's Rule versus Biomechanical Models
Minamino, Ryoko; Tateno, Masaki
2014-01-01
This study examined Leonardo da Vinci's rule (i.e., the sum of the cross-sectional area of all tree branches above a branching point at any height is equal to the cross-sectional area of the trunk or the branch immediately below the branching point) using simulations based on two biomechanical models: the uniform stress and elastic similarity models. Model calculations of the daughter/mother ratio (i.e., the ratio of the total cross-sectional area of the daughter branches to the cross-sectional area of the mother branch at the branching point) showed that both biomechanical models agreed with da Vinci's rule when the branching angles of daughter branches and the weights of lateral daughter branches were small; however, the models deviated from da Vinci's rule as the weights and/or the branching angles of lateral daughter branches increased. The calculated values of the two models were largely similar but differed in some ways. Field measurements of Fagus crenata and Abies homolepis also fit this trend, wherein models deviated from da Vinci's rule with increasing relative weights of lateral daughter branches. However, this deviation was small for a branching pattern in nature, where empirical measurements were taken under realistic measurement conditions; thus, da Vinci's rule did not critically contradict the biomechanical models in the case of real branching patterns, though the model calculations described the contradiction between da Vinci's rule and the biomechanical models. The field data for Fagus crenata fit the uniform stress model best, indicating that stress uniformity is the key constraint of branch morphology in Fagus crenata rather than elastic similarity or da Vinci's rule. On the other hand, mechanical constraints are not necessarily significant in the morphology of Abies homolepis branches, depending on the number of daughter branches. Rather, these branches were often in agreement with da Vinci's rule. PMID:24714065
NASA Astrophysics Data System (ADS)
Onorato, P.
2011-03-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P Feynman and developed by E F Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of propagation amplitude is discussed for unbounded systems. These semiclassical results are obtained when the SOP is limited to the trajectories classically allowed. EBK semiclassical quantization and the topological Maslov index are used to deduce the correct quantum mechanical results for systems which live in a two-dimensional world as quantum dots and quantum rings. In the latter systems, the semiclassical propagation amplitude is used to discuss the Aharonov-Bohm effect. The development involves only elementary calculus and also provides a theoretical introduction to the quantum nature of low-dimensional nanostructures.
Enhanced Cumulative Sum Charts for Monitoring Process Dispersion
Abujiya, Mu’azu Ramat; Riaz, Muhammad; Lee, Muhammad Hisyam
2015-01-01
The cumulative sum (CUSUM) control chart is widely used in industry for the detection of small and moderate shifts in process location and dispersion. For efficient monitoring of process variability, we present several CUSUM control charts for monitoring changes in standard deviation of a normal process. The newly developed control charts based on well-structured sampling techniques - extreme ranked set sampling, extreme double ranked set sampling and double extreme ranked set sampling, have significantly enhanced CUSUM chart ability to detect a wide range of shifts in process variability. The relative performances of the proposed CUSUM scale charts are evaluated in terms of the average run length (ARL) and standard deviation of run length, for point shift in variability. Moreover, for overall performance, we implore the use of the average ratio ARL and average extra quadratic loss. A comparison of the proposed CUSUM control charts with the classical CUSUM R chart, the classical CUSUM S chart, the fast initial response (FIR) CUSUM R chart, the FIR CUSUM S chart, the ranked set sampling (RSS) based CUSUM R chart and the RSS based CUSUM S chart, among others, are presented. An illustrative example using real dataset is given to demonstrate the practicability of the application of the proposed schemes. PMID:25901356
Rarefied-continuum gas dynamics transition for SUMS project
NASA Technical Reports Server (NTRS)
Cheng, Sin-I
1989-01-01
This program is to develop an analytic method for reducing SUMS data for the determination of the undisturbed atmosphere conditions ahead of the shuttle along its descending trajectory. It is divided into an internal flow problem, an external flow problem and their matching conditions. Since the existing method of Direct Simulation Monte Carlo (DSMC) failed completely for the internal flow problem, the emphasis is on the internal flow of a highly non-equilibrium, rarefied air through a short tube of a diameter much less than the gaseous mean free path. A two fluid model analysis of this internal flow problem has been developed and studied with typical results illustrated. A computer program for such an analysis and a technical paper published in Lecture Notes in Physics No. 323 (1989) are included as Appendices 3 and 4. A proposal for in situ determination of the surface accommodation coefficients sigma sub t and sigma e is included in Appendix 5 because of their importance in quantitative data reduction. A two fluid formulation for the external flow problem is included as Appendix 6 and a review article for AIAA on Hypersonic propulsion, much dependent on ambient atmospheric density, is also included as Appendix 7.
Maintaining genetic integrity in aging: a zero sum game.
Suh, Yousin; Vijg, Jan
2006-01-01
Aging of somatic cells can be defined as the gradual loss of the information embedded in the global and local properties of complex macromolecular networks. This loss of information may reflect the dynamic interplay between stochastic factors, such as the accumulation of unrepaired somatic damage, and gene-encoded programmatic responses. This would ultimately result in loss of function, impaired response to environmental challenge, and a progressively increased incidence of disease. Here the authors present the case for aging as a continuous battle between maintaining genomic integrity and ensuring sufficient cell functional mass. Focusing on aging of the liver in rodents, evidence is presented that normal aging is associated with a gradual accumulation of random alterations in the DNA of the genome as a consequence of imperfect DNA repair and a decrease in the rate of DNA damage-induced apoptosis. Apoptosis is the cell's genome maintenance mechanism of last resort and an imbalance towards apoptosis can contribute to manifestations of aging-related phenotypes, as exemplified by mouse models of premature aging due to genetic defects in genome maintenance. Prospects to reset the clock in this zero sum game between survival and the maintenance of phenotypic integrity will be discussed. PMID:16677100
Cumulative sum quality control for calibrated breast density measurements
Heine, John J.; Cao Ke; Beam, Craig
2009-12-15
Purpose: Breast density is a significant breast cancer risk factor. Although various methods are used to estimate breast density, there is no standard measurement for this important factor. The authors are developing a breast density standardization method for use in full field digital mammography (FFDM). The approach calibrates for interpatient acquisition technique differences. The calibration produces a normalized breast density pixel value scale. The method relies on first generating a baseline (BL) calibration dataset, which required extensive phantom imaging. Standardizing prospective mammograms with calibration data generated in the past could introduce unanticipated error in the standardized output if the calibration dataset is no longer valid. Methods: Sample points from the BL calibration dataset were imaged approximately biweekly over an extended timeframe. These serial samples were used to evaluate the BL dataset reproducibility and quantify the serial calibration accuracy. The cumulative sum (Cusum) quality control method was used to evaluate the serial sampling. Results: There is considerable drift in the serial sample points from the BL calibration dataset that is x-ray beam dependent. Systematic deviation from the BL dataset caused significant calibration errors. This system drift was not captured with routine system quality control measures. Cusum analysis indicated that the drift is a sign of system wear and eventual x-ray tube failure. Conclusions: The BL calibration dataset must be monitored and periodically updated, when necessary, to account for sustained system variations to maintain the calibration accuracy.
Investigating buried polymer interfaces using sum frequency generation vibrational spectroscopy
Chen, Zhan
2010-01-01
This paper reviews recent progress in the studies of buried polymer interfaces using sum frequency generation (SFG) vibrational spectroscopy. Both buried solid/liquid and solid/solid interfaces involving polymeric materials are discussed. SFG studies of polymer/water interfaces show that different polymers exhibit varied surface restructuring behavior in water, indicating the importance of probing polymer/water interfaces in situ. SFG has also been applied to the investigation of interfaces between polymers and other liquids. It has been found that molecular interactions at such polymer/liquid interfaces dictate interfacial polymer structures. The molecular structures of silane molecules, which are widely used as adhesion promoters, have been investigated using SFG at buried polymer/silane and polymer/polymer interfaces, providing molecular-level understanding of polymer adhesion promotion. The molecular structures of polymer/solid interfaces have been examined using SFG with several different experimental geometries. These results have provided molecular-level information about polymer friction, adhesion, interfacial chemical reactions, interfacial electronic properties, and the structure of layer-by-layer deposited polymers. Such research has demonstrated that SFG is a powerful tool to probe buried interfaces involving polymeric materials, which are difficult to study by conventional surface sensitive analytical techniques. PMID:21113334
Rational trigonometric approximations using Fourier series partial sums
NASA Technical Reports Server (NTRS)
Geer, James F.
1993-01-01
A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.
Optimal methods for calculating classification images: weighted sums.
Murray, Richard F; Bennett, Patrick J; Sekuler, Allison B
2002-01-01
In signal detection theory, an observer's responses are often modeled as being based on a decision variable obtained by cross-correlating the stimulus with a template, possibly after corruption by external and internal noise. The response classification method estimates an observer's template by measuring the influence of each pixel of external noise on the observer's responses. A map that shows the influence of each pixel is called a classification image. Other authors have shown how to calculate classification images from external noise fields, but the optimal calculation has never been determined, and the quality of the resulting classification images has never been evaluated. Here we derive the optimal weighted sum of noise fields for calculating classification images in several experimental designs, and we derive the signal-to-noise ratio (SNR) of the resulting classification images. Using the expressions for the SNR, we show how to choose experimental parameters, such as the observer's performance level and the external noise power, to obtain classification images with a high SNR. We discuss two-alternative identification experiments in which the stimulus is presented at one or more contrast levels, in which each stimulus is presented twice so that we can estimate the power of the internal noise from the consistency of the observer's responses, and in which the observer rates the confidence of his responses. We illustrate these methods in a series of contrast increment detection experiments.
Sum frequency generation studies of membrane transport phenomena
Dyer, R.B.; Shreve, A.P.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The objective of this work is to study the transport of protons and ions across biological membranes, one of the most fundamental processes in living organisms, critical for energy transduction in respiration and photosynthesis and for a wide variety of cellular signal transduction events. Membrane protein structure and function, in particular proton and ion pumping are poorly understood. The authors have developed sum frequency generation (SFG) spectroscopy for the study of membrane phenomena, a nonlinear spectroscopic technique that is uniquely sensitive to interfaces and with demonstrated structural specificity. They have used SFG and conventional vibrational spectroscopic approaches to study proton transport processes in cytochrome c oxidase. A key finding has been the identification of vibrational modes associated with proton labile groups, including a glutamic acid near the redox active binuclear center and structural waters. These groups are sensitive to the ligation and redox states of the metal centers and hence are ideal candidates for coupling redox energy to proton transport processes.
Sum-frequency generation echo and grating from interface
Volkov, Victor
2014-10-14
The work addresses spectroscopy of fourth-order Sum Frequency Generation Echo and Grating responses as an experimental tool to study structure and dynamics at interfaces. First, it addresses experimental geometry to extract background-free fourth-order Echo and Grating responses. Further, the article provides the analytical expressions of the response functions for these nonlinearities. The derived expressions are used to model the χ{sup (4)} two-dimensional spectral responses of a hydrated methyl acetate, which resembles a hydrated carbonyl moiety at the polar outer side of a phospholipid membrane. Orientation, transition dipole moments, and Raman tensors are obtained from the results of classical and quantum calculations, respectively. The numerical studies for the nonlinear responses under different polarization schemes and timings suggest the possibility of securely factoring of spectral contributions of χ{sub YYYZX} and χ{sub YYYZY} macroscopic susceptibilities. As such, the nonlinearities provide an experimental perspective on orientation of a generic (low-symmetry) molecular system at interfaces. Besides, the spectral properties of the tensors may reflect correlations of the in-plane and out-of-plane field components specific to the interface. For the case of a phospholipid membrane, the experiment would address in-plane and out-of-plane anisotropy of hydrogen bonding and related dynamics.
Permutation-symmetry related selection rules in spinor quantum gases
NASA Astrophysics Data System (ADS)
Yurovsky, Vladimir
2014-05-01
Selection rules constraining possible transitions between states of quantum systems can be derived from the system symmetry. Invariance over permutations of indistinguishable particles, contained in each physical system, is one of the basic symmetries. Consider a many-body system with separable spin and spatial degrees of freedom of particles with arbitrary spins s. Eigenfunctions of such systems can be expressed as a sum of products of spin and spatial functions, which form irreducible representations (irreps) of the symmetric group. The quantum numbers are the Young diagrams λ = [λ1 , ... ,λ2 s + 1 ] . The selection rules for a general k-body interactions allow transitions between the states λ and λ' only if ∑m=12s+1 |λm -λm'| <= 2 k . For s = 1 / 2 , the Young diagrams are unambiguously related to the total spin, and if k = 1 , we get the conventional selection rule for dipole transitions. However, if s > 1 / 2 , the rules cannot be expressed in terms of spins. The selection rules provide a way of control over the formation of many-body entangled states, belonging to multidimensional, non-Abelian irreps of the symmetric group. The effects can be observed with spinor atoms in an optical lattice in the Mott-insulator regime.
Caregivers program. Final rule.
2015-01-01
The Department of Veterans Affairs (VA) adopts, with changes, the interim final rule concerning VA's Program of Comprehensive Assistance for Family Caregivers. VA administers this program to provide certain medical, travel, training, and financial benefits to caregivers of certain veterans and servicemembers who were seriously injured during service on or after September 11, 2001. Also addressed in this rulemaking is the Program of General Caregiver Support Services that provides support services to caregivers of veterans from all eras who are enrolled in the VA health care system. Specifically, changes in this final rule include a requirement that Veterans be notified in writing should a Family Caregiver request revocation (to no longer be a Family Caregiver), an extension of the application timeframe from 30 days to 45 days for a Family Caregiver, and a change in the stipend calculation to ensure that Primary Family Caregivers do not experience unexpected decreases in stipend amounts from year to year. PMID:25581943
Disagreement Rules, Referral Rules and the Spanish Feminine Article "el."
ERIC Educational Resources Information Center
Harris, J. W.
1987-01-01
The Spanish feminine article /el/, ordinarily the singular masculine definite article, has been used as evidence of the need for obligatory disagreement rules. Others explain the anamoly by means of referral rules. A third solution is suggested: an allomorphy rule which can be interpreted syntactically or phonologically. (LMO)
Parental Rule Socialization for Preventive Health and Adolescent Rule Compliance
ERIC Educational Resources Information Center
Bylund, Carma L.; Baxter, Leslie A.; Imes, Rebecca S.; Wolf, Bianca
2010-01-01
This study examined family rules about nutrition, exercise, and sun protection in 164 parent-young adult children dyads. Both parents and their young adult children independently reported on health rules that they perceived throughout their child's adolescent years and the extent to which the rules were articulated, violations sanctioned, and…
Sum1-1: A Suppressor of Silencing Defects in Saccharomyces Cerevisiae
Laurenson, P.; Rine, J.
1991-01-01
The repression of transcription of the silent mating-type locus HMRa in the yeast Saccharomyces cerevisiae requires the four SIR proteins, histone H4 and a flanking site designated HMR-E. The SUM1-1 mutation alleviated the need for many of these components in transcriptional repression. In the absence of each of the SIR proteins, SUM1-1 restored repression in MATα strains; thus, SUM1-1 appeared to bypass the need for the SIR genes in repression of HMRa. Repression was not specific to the genes normally present at HMR, since the TRP1 gene placed at HMR was repressed by SUM1-1 in a sir3 strain. Therefore, like the mechanism of silencing normally used at HMR, silencing by SUM1-1 was gene-nonspecific. SUM1-1 suppressed point mutations in histone H4, but failed to suppress strongly a deletion mutation in histone H4. Similarly, SUM1-1 suppressed mutations in the three known elements of HMR-E, but was unable to suppress a deletion of HMR-E. These epistasis analyses implied that the functions required for repression at HMR can be ordered, with the SIR genes and silencer elements acting upstream of SUM1-1. SUM1-1 itself may function at the level of chromatin in the assembly of inactive DNA at the silent mating-type loci. PMID:1752414
Modifications of Team Sports Rules.
ERIC Educational Resources Information Center
Rokosz, Francis M.
In general, there are two reasons for modifying the rules in sport activities: (1) to meet a specific objective or (2) to solve a perceived problem. The sense of the original game is usually not altered significantly because the number of rule changes is kept to a minimum. Changes in rules may be made for administrative or financial reasons, or to…
NASA Technical Reports Server (NTRS)
Stahl, H. Philip
2014-01-01
Based on 30 years of optical testing experience, a lot of mistakes, a lot of learning and a lot of experience, I have defined seven guiding principles for optical testing - regardless of how small or how large the optical testing or metrology task. GUIDING PRINCIPLES 1. Fully Understand the Task 2. Develop an Error Budget 3. Continuous Metrology Coverage 4. Know where you are 5. 'Test like you fly' 6. Independent Cross-Checks 7. Understand All Anomalies. These rules have been applied with great success to the in-process optical testing and final specification compliance testing of the JWST mirrors.
NASA Technical Reports Server (NTRS)
Stahl, H. Philip
2014-01-01
Based on 30 years of optical testing experience, a lot of mistakes, a lot of learning and a lot of experience, I have defined seven guiding principles for optical testing - regardless of how small or how large the optical testing or metrology task: Fully Understand the Task, Develop an Error Budget, Continuous Metrology Coverage, Know where you are, Test like you fly, Independent Cross-Checks, Understand All Anomalies. These rules have been applied with great success to the inprocess optical testing and final specification compliance testing of the JWST mirrors.
NASA Technical Reports Server (NTRS)
Stahl, H. Philip
2014-01-01
Based on 30 years of optical testing experience, a lot of mistakes, a lot of learning and a lot of experience, I have defined seven guiding principles for optical testing - regardless of how small or how large the optical testing or metrology task. GUIDING PRINCIPLES 1.Fully Understand the Task 2.Develop an Error Budget 3.Continuous Metrology Coverage 4.Know where you are 5. 'Test like you fly' 6.Independent Cross-Checks 7.Understand All Anomalies. These rules have been applied with great success to the in-process optical testing and final specification compliance testing of the JWST mirrors.
24 CFR 570.513 - Lump sum drawdown for financing of property rehabilitation activities.
Code of Federal Regulations, 2010 CFR
2010-04-01
... DEVELOPMENT BLOCK GRANTS Grant Administration § 570.513 Lump sum drawdown for financing of property... 24 Housing and Urban Development 3 2010-04-01 2010-04-01 false Lump sum drawdown for financing of property rehabilitation activities. 570.513 Section 570.513 Housing and Urban Development...
Stochastic Ordering of the Latent Trait by the Sum Score Under Various Polytomous IRT Models
ERIC Educational Resources Information Center
van der Ark, L. Andries
2005-01-01
The sum score is often used to order respondents on the latent trait measured by the test. Therefore, it is desirable that under the chosen model the sum score stochastically orders the latent trait. It is known that unlike dichotomous item response theory (IRT) models, most polytomous IRT models do not imply stochastic ordering. It is unknown,…
Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers
NASA Astrophysics Data System (ADS)
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2011-09-01
We discuss algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. For a certain set of 12 such sums, we show that any two numbers are algebraically independent, and that any three are algebraically independent except for those in 22 exceptional triplets. We explicitly present algebraic relations for some of these exceptional cases.
Congruences for a Class of Alternating Lacunary Sums of Binomial Coefficients
NASA Astrophysics Data System (ADS)
Dilcher, Karl
2007-10-01
An 1876 theorem of Hermite, later extended by Bachmann, gives congruences modulo primes for lacunary sums over the rows of Pascal's triangle. This paper gives an analogous result for alternating sums over a certain class of rows. The proof makes use of properties of certain linear recurrences.
A Comparison of Heuristic Procedures for Minimum within-Cluster Sums of Squares Partitioning
ERIC Educational Resources Information Center
Brusco, Michael J.; Steinley, Douglas
2007-01-01
Perhaps the most common criterion for partitioning a data set is the minimization of the within-cluster sums of squared deviation from cluster centroids. Although optimal solution procedures for within-cluster sums of squares (WCSS) partitioning are computationally feasible for small data sets, heuristic procedures are required for most practical…
SUM (Service Unit Management): An Organizational Approach To Improved Patient Care.
ERIC Educational Resources Information Center
Jelinek, Richard C.; And Others
To evaluate the effectiveness of Service Unit Management (SUM) in reducing costs, improving quality of care, saving professional nursing time, increasing personnel satisfaction, and setting a stage for further improvements, a national questionnaire survey identified the characteristics of SUM units, and compared the performance of a total of 55…
Why the Faulhaber Polynomials Are Sums of Even or Odd Powers of (n + 1/2)
ERIC Educational Resources Information Center
Hersh, Reuben
2012-01-01
By extending Faulhaber's polynomial to negative values of n, the sum of the p'th powers of the first n integers is seen to be an even or odd polynomial in (n + 1/2) and therefore expressible in terms of the sum of the first n integers.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-09-16
... AFFAIRS Proposed Information Collection (Claim for One Sum Payment (Government Life Insurance)); Comment.... Claim for One Sum Payment (Government Life Insurance), VA Form 29-4125. b. Claim for Monthly Payments (National Service Life Insurance), VA Form 29-4125a. c. Claim for Monthly Payments (United States...
Federal Register 2010, 2011, 2012, 2013, 2014
2013-03-26
... AFFAIRS Proposed Information Collection (Claim for One Sum Payment (Government Life Insurance)); Comment.... Claim for One Sum Payment (Government Life Insurance), VA Form 29-4125. b. Claim for Monthly Payments (National Service Life Insurance), VA Form 29-4125a. c. Claim for Monthly Payments (United States...
Federal Register 2010, 2011, 2012, 2013, 2014
2013-08-27
... AFFAIRS Agency Information Collection (Claim for One Sum Payment (Government Life Insurance)) Activities... for One Sum Payment (Government Life Insurance), VA Form 29-4125. ] b. Claim for Monthly Payments (National Service Life Insurance), VA Form 29-4125a. c. Claim for Monthly Payments (United States...
27 CFR 19.957 - Instructions to compute bond penal sum.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Instructions to compute bond penal sum. 19.957 Section 19.957 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX... Fuel Use Bonds § 19.957 Instructions to compute bond penal sum. (a) Medium plants. To find the...
The Product and Quotient Rules Revisited
ERIC Educational Resources Information Center
Eggleton, Roger; Kustov, Vladimir
2011-01-01
Mathematical elegance is illustrated by strikingly parallel versions of the product and quotient rules of basic calculus, with some applications. Corresponding rules for second derivatives are given: the product rule is familiar, but the quotient rule is less so.
Code of Federal Regulations, 2010 CFR
2010-01-01
... WELFARE HORSE PROTECTION REGULATIONS § 11.3 Scar rule. The scar rule applies to all horses born on or after October 1, 1975. Horses subject to this rule that do not meet the following scar rule...
Unruh, Gregory C
2008-02-01
Sustainability, defined by natural scientists as the capacity of healthy ecosystems to function indefinitely, has become a clarion call for business. Leading companies have taken high-profile steps toward achieving it: Wal-Mart, for example, with its efforts to reduce packaging waste, and Nike, which has removed toxic chemicals from its shoes. But, says Unruh, the director of Thunderbird's Lincoln Center for Ethics in Global Management, sustainability is more than an endless journey of incremental steps. It is a destination, for which the biosphere of planet Earth--refined through billions of years of trial and error--is a perfect model. Unruh distills some lessons from the biosphere into three rules: Use a parsimonious palette. Managers can rethink their sourcing strategies and dramatically simplify the number and types of materials their companies use in production, making recycling cost-effective. After the furniture manufacturer Herman Miller discovered that its leading desk chair had 200 components made from more than 800 chemical compounds, it designed an award-winning successor whose far more limited materials palette is 96% recyclable. Cycle up, virtuously. Manufacturers should design recovery value into their products at the outset. Shaw Industries, for example, recycles the nylon fiber from its worn-out carpet into brand-new carpet tile. Exploit the power of platforms. Platform design in industry tends to occur at the component level--but the materials in those components constitute a more fundamental platform. Patagonia, by recycling Capilene brand performance underwear, has achieved energy costs 76% below those for virgin sourcing. Biosphere rules can teach companies how to build ecologically friendly products that both reduce manufacturing costs and prove highly attractive to consumers. And managers need not wait for a green technological revolution to implement them.
Unruh, Gregory C
2008-02-01
Sustainability, defined by natural scientists as the capacity of healthy ecosystems to function indefinitely, has become a clarion call for business. Leading companies have taken high-profile steps toward achieving it: Wal-Mart, for example, with its efforts to reduce packaging waste, and Nike, which has removed toxic chemicals from its shoes. But, says Unruh, the director of Thunderbird's Lincoln Center for Ethics in Global Management, sustainability is more than an endless journey of incremental steps. It is a destination, for which the biosphere of planet Earth--refined through billions of years of trial and error--is a perfect model. Unruh distills some lessons from the biosphere into three rules: Use a parsimonious palette. Managers can rethink their sourcing strategies and dramatically simplify the number and types of materials their companies use in production, making recycling cost-effective. After the furniture manufacturer Herman Miller discovered that its leading desk chair had 200 components made from more than 800 chemical compounds, it designed an award-winning successor whose far more limited materials palette is 96% recyclable. Cycle up, virtuously. Manufacturers should design recovery value into their products at the outset. Shaw Industries, for example, recycles the nylon fiber from its worn-out carpet into brand-new carpet tile. Exploit the power of platforms. Platform design in industry tends to occur at the component level--but the materials in those components constitute a more fundamental platform. Patagonia, by recycling Capilene brand performance underwear, has achieved energy costs 76% below those for virgin sourcing. Biosphere rules can teach companies how to build ecologically friendly products that both reduce manufacturing costs and prove highly attractive to consumers. And managers need not wait for a green technological revolution to implement them. PMID:18314639
Debra Jezouit; Frank Rambo
2005-07-01
On May 12, 2005, EPA promulgated the Clean Air Interstate Rule, which overhauls and expands the scope of air emissions trading programs in the eastern United States. The rule imposes statewide caps on emissions of nitrogen oxides and sulfur dioxide to be introduced in two phases, beginning in 2009. This article briefly explains the background leading up to the rule and summarizes its key findings and requirements. 2 refs., 1 fig., 1 tab.
Empirically derived injury prevention rules.
Peterson, L; Schick, B
1993-01-01
This study describes a set of empirically derived safety rules that if followed, would have prevented the occurrence of minor injuries. Epidemiologists have criticized behavioral interventions as increasing "safe" behavior but failing to demonstrate a decrease in injury. The present study documents retrospectively the link between safe behavior and injury. It demonstrates that these empirically derived rules are very similar to rules for the prevention of serious injury. The study also shows that these rules are not widely accepted and implemented by parents. Suggestions for future research in this area are advanced. PMID:8307829
Olasov, Ben; Sim, Ida
2006-01-01
RuleEd is a web-based editing environment which enables clinical trial eligibility rules entered as free text to be represented as a series of terms mapped to unique concepts in a controlled vocabulary. RuleEd provides interfaces for creating and refining concept mappings for terms within rules and disambiguating multiply-mapped terms. A combination of inter-active and non-interactive methods enable authors to specify eligibility rule representations with a fine level of control.
Developmental Disabilities Program. Final rule.
2015-07-27
This rule implements the Developmental Disabilities Assistance and Bill of Rights Act of 2000. The previous regulations were completed in 1997 before the current law was passed. The rule will align the regulations and current statute and will provide guidance to AIDD grantees. PMID:26214859
Michael Rossler
2005-07-01
Coming into force on July 15, 2005, the US Clean Air Mercury Rule will use a market-based cap-and-trade approach under Section 111 of the Clean Air Act to reduce mercury emissions from the electric power sector. This article provides a comprehensive summary of the new rule. 14 refs., 2 tabs.
Examining Tennessee's collateral source rule.
Regan, Judith; Hadley, Edward; Regan, William M
2008-11-01
The common law collateral source rule was established to prevent the defendant from benefiting from their wrongful actions. Despite a trend in the United States to limit the effects of the collateral source rule, the rule remains in force in courts of the State of Tennessee. However, to assist with the malpractice crisis, the legislature prohibited this rule by statute in regards to the Medical Malpractice Act. Although this statutory prohibition of the collateral source rule worked to lessen verdicts in malpractice cases after passage, the availability of consortium damages resulting from Jordan v. Baptist Three Rivers Hospital in 1999 has worked to drive verdicts substantially higher. Regardless the Medical Malpractice Act has been held as constitutional and has been clarified through several recent Tennessee court decisions. PMID:19024250
5 CFR 550.1204 - Projecting the lump-sum leave period.
Code of Federal Regulations, 2010 CFR
2010-01-01
... this chapter; or credit hours accumulated under an alternative work schedule established under 5 U.S.C... annual leave to the employee's credit. The agency must project the lump-sum period leave beginning on...
Casimir energy for a double spherical shell: A global mode sum approach
NASA Astrophysics Data System (ADS)
Miltão, M. S. R.
2008-09-01
In this work we study the configuration of two perfectly conducting spherical shells. This is a problem of basic importance to make possible development of experimental apparatuses that they make possible to measure the spherical Casimir effect, an open subject. We apply the mode sum method via cutoff exponential function regularization with two independent parameters: one to regularize the infinite order sum of the Bessel functions; other, to regularize the integral that becomes related, due to the argument theorem, with the infinite zero sum of the Bessel functions. We obtain a general expression of the Casimir energy as a quadrature sum. We investigate two immediate limit cases as a consistency test of the expression obtained: that of a spherical shell and that of two parallel plates. In the approximation of a thin spherical shell we obtain an expression that allows to relate our result with that of the proximity-force approximation, supplying a correction to this result.
An exact formulation of the time-ordered exponential using path-sums
Giscard, P.-L.; Lui, K.; Thwaite, S. J.; Jaksch, D.
2015-05-15
We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitude of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.
5 CFR 838.235 - Payment of lump-sum awards.
Code of Federal Regulations, 2010 CFR
2010-01-01
... REGULATIONS (CONTINUED) COURT ORDERS AFFECTING RETIREMENT BENEFITS Procedures for Processing Court Orders Affecting Employee Annuities Payment Procedures § 838.235 Payment of lump-sum awards. If a court...
5 CFR 838.235 - Payment of lump-sum awards.
Code of Federal Regulations, 2014 CFR
2014-01-01
... REGULATIONS (CONTINUED) COURT ORDERS AFFECTING RETIREMENT BENEFITS Procedures for Processing Court Orders Affecting Employee Annuities Payment Procedures § 838.235 Payment of lump-sum awards. If a court...
5 CFR 838.235 - Payment of lump-sum awards.
Code of Federal Regulations, 2013 CFR
2013-01-01
... REGULATIONS (CONTINUED) COURT ORDERS AFFECTING RETIREMENT BENEFITS Procedures for Processing Court Orders Affecting Employee Annuities Payment Procedures § 838.235 Payment of lump-sum awards. If a court...
Optimal approximations for risk measures of sums of lognormals based on conditional expectations
NASA Astrophysics Data System (ADS)
Vanduffel, S.; Chen, X.; Dhaene, J.; Goovaerts, M.; Henrard, L.; Kaas, R.
2008-11-01
In this paper we investigate the approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S|[Lambda
20 CFR 341.2 - Sum or damages paid or payable.
Code of Federal Regulations, 2011 CFR
2011-04-01
... INSURANCE ACT STATUTORY LIEN WHERE SICKNESS BENEFITS PAID § 341.2 Sum or damages paid or payable. (a) The...-Fault” personal-injury protection benefits or any other benefits paid under a health, sickness,...
20 CFR 341.2 - Sum or damages paid or payable.
Code of Federal Regulations, 2014 CFR
2014-04-01
... INSURANCE ACT STATUTORY LIEN WHERE SICKNESS BENEFITS PAID § 341.2 Sum or damages paid or payable. (a) The...-Fault” personal-injury protection benefits or any other benefits paid under a health, sickness,...
20 CFR 341.2 - Sum or damages paid or payable.
Code of Federal Regulations, 2012 CFR
2012-04-01
... INSURANCE ACT STATUTORY LIEN WHERE SICKNESS BENEFITS PAID § 341.2 Sum or damages paid or payable. (a) The...-Fault” personal-injury protection benefits or any other benefits paid under a health, sickness,...
20 CFR 341.2 - Sum or damages paid or payable.
Code of Federal Regulations, 2013 CFR
2013-04-01
... INSURANCE ACT STATUTORY LIEN WHERE SICKNESS BENEFITS PAID § 341.2 Sum or damages paid or payable. (a) The...-Fault” personal-injury protection benefits or any other benefits paid under a health, sickness,...
Domurat, Artur; Kowalczuk, Olga; Idzikowska, Katarzyna; Borzymowska, Zuzanna; Nowak-Przygodzka, Marta
2015-01-01
This paper has two aims. First, we investigate how often people make choices conforming to Bayes’ rule when natural sampling is applied. Second, we show that using Bayes’ rule is not necessary to make choices satisfying Bayes’ rule. Simpler methods, even fallacious heuristics, might prescribe correct choices reasonably often under specific circumstances. We considered elementary situations with binary sets of hypotheses and data. We adopted an ecological approach and prepared two-stage computer tasks resembling natural sampling. Probabilistic relations were inferred from a set of pictures, followed by a choice which was made to maximize the chance of a preferred outcome. Use of Bayes’ rule was deduced indirectly from choices. Study 1 used a stratified sample of N = 60 participants equally distributed with regard to gender and type of education (humanities vs. pure sciences). Choices satisfying Bayes’ rule were dominant. To investigate ways of making choices more directly, we replicated Study 1, adding a task with a verbal report. In Study 2 (N = 76) choices conforming to Bayes’ rule dominated again. However, the verbal reports revealed use of a new, non-inverse rule, which always renders correct choices, but is easier than Bayes’ rule to apply. It does not require inversion of conditions [transforming P(H) and P(D|H) into P(H|D)] when computing chances. Study 3 examined the efficiency of three fallacious heuristics (pre-Bayesian, representativeness, and evidence-only) in producing choices concordant with Bayes’ rule. Computer-simulated scenarios revealed that the heuristics produced correct choices reasonably often under specific base rates and likelihood ratios. Summing up we conclude that natural sampling results in most choices conforming to Bayes’ rule. However, people tend to replace Bayes’ rule with simpler methods, and even use of fallacious heuristics may be satisfactorily efficient. PMID:26347676
Domurat, Artur; Kowalczuk, Olga; Idzikowska, Katarzyna; Borzymowska, Zuzanna; Nowak-Przygodzka, Marta
2015-01-01
This paper has two aims. First, we investigate how often people make choices conforming to Bayes' rule when natural sampling is applied. Second, we show that using Bayes' rule is not necessary to make choices satisfying Bayes' rule. Simpler methods, even fallacious heuristics, might prescribe correct choices reasonably often under specific circumstances. We considered elementary situations with binary sets of hypotheses and data. We adopted an ecological approach and prepared two-stage computer tasks resembling natural sampling. Probabilistic relations were inferred from a set of pictures, followed by a choice which was made to maximize the chance of a preferred outcome. Use of Bayes' rule was deduced indirectly from choices. Study 1 used a stratified sample of N = 60 participants equally distributed with regard to gender and type of education (humanities vs. pure sciences). Choices satisfying Bayes' rule were dominant. To investigate ways of making choices more directly, we replicated Study 1, adding a task with a verbal report. In Study 2 (N = 76) choices conforming to Bayes' rule dominated again. However, the verbal reports revealed use of a new, non-inverse rule, which always renders correct choices, but is easier than Bayes' rule to apply. It does not require inversion of conditions [transforming P(H) and P(D|H) into P(H|D)] when computing chances. Study 3 examined the efficiency of three fallacious heuristics (pre-Bayesian, representativeness, and evidence-only) in producing choices concordant with Bayes' rule. Computer-simulated scenarios revealed that the heuristics produced correct choices reasonably often under specific base rates and likelihood ratios. Summing up we conclude that natural sampling results in most choices conforming to Bayes' rule. However, people tend to replace Bayes' rule with simpler methods, and even use of fallacious heuristics may be satisfactorily efficient.
26 CFR 1.167(b)-3 - Sum of the years-digits method.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 26 Internal Revenue 2 2011-04-01 2011-04-01 false Sum of the years-digits method. 1.167(b)-3 Section 1.167(b)-3 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) INCOME TAX (CONTINUED) INCOME TAXES (CONTINUED) Itemized Deductions for Individuals and Corporations § 1.167(b)-3 Sum of the years-digits method....
On estimating mean lifetimes by a weighted sum of lifetime measurements
NASA Astrophysics Data System (ADS)
Prosper, Harrison Bertrand
1987-10-01
Given N lifetime measurements an estimate of the mean lifetime can be obtained from a weighted sum of these measurements. We derive exact expressions for the probability density function, the moment-generating function, and the cumulative distribution function for the weighted sum. We indicate how these results might be used in the estimation of particle lifetimes. The probability distribution function of Yost for the distribution of lifetime measurements with finite measurement error is our starting point.
Teleportation-based number-state manipulation with number-sum measurement
Kitagawa, Akira; Yamamoto, Katsuji
2003-10-01
We examine various manipulations of photon number states which can be implemented by teleportation technique with number-sum measurement. The preparations of the Einstein-Podolsky-Rosen resources as well as the number-sum measurement resulting in projection to certain Bell state may be done conditionally with linear optical elements, i.e., beam splitters, phase shifters, and zero-one-photon detectors. Squeezed vacuum states are used as primary entanglement resource, while single-photon sources are not required.
McKie, John; Richardson, Jeff
2003-06-01
Jonsen coined the term "Rule of Rescue"(RR) to describe the imperative people feel to rescue identifiable individuals facing avoidable death. In this paper we attempt to draw a more detailed picture of the RR, identifying its conflict with cost-effectiveness analysis, the preference it entails for identifiable over statistical lives, the shock-horror response it elicits, the preference it entails for lifesaving over non-lifesaving measures, its extension to non-life-threatening conditions, and whether it is motivated by duty or sympathy. We also consider the measurement problems it raises, and argue that quantifying the RR would probably require a two-stage procedure. In the first stage the size of the individual utility gain from a health intervention would be assessed using a technique such as the Standard Gamble or the Time Trade-Off, and in the second the social benefits arising from the RR would be quantified employing the Person Trade-Off. We also consider the normative status of the RR. We argue that it can be defended from a utilitarian point of view, on the ground that rescues increase well-being by reinforcing people's belief that they live in a community that places great value upon life. However, utilitarianism has long been criticised for failing to take sufficient account of fairness, and the case is no different here: fairness requires that we do not discriminate between individuals on morally irrelevant grounds, whereas being "identifiable" does not seem to be a morally relevant ground for discrimination.
The sum-connectivity index--an additive variant of the Randic connectivity index.
Lučić, Bono; Sović, Ivan; Batista, Jadranko; Skala, Karolj; Plavšić, Dejan; Vikić-Topić, Drazen; Bešlo, Drago; Nikolić, Sonja; Trinajstić, Nenad
2013-06-01
This review discusses structure-property modeling applications of a novel variant of the Randic connectivity index that is called the sum-connectivity index. We compare published one-descriptor quantitative structure-property relationship (QSPR) models obtained with the new sum-connectivity index and with the Randic connectivity index, called here the product-connectivity index. Additionally, the efficiency of both variants of connectivity indices in QSPR modeling is tested on five datasets of alkanes and two datasets of polycyclic hydrocarbons. Several physicochemical properties of alkanes (i.e. boiling and melting points, retention index, molar volume, molar refraction, heat of vaporization, standard Gibbs energy of formation, critical temperature, critical pressure, surface tension, density) and π- electronic energies of two sets of polycyclic hydrocarbons were correlated with the product- and sum-connectivity indices. A comparison of these QSPR models shows that both variants of connectivity indices are equivalent, and only slightly (but not significantly) better results are obtained with the sum-connectivity index. Inter-correlations between the product- and sum-connectivity indices are mostly linear with a slope very close to 1.0 for alkanes, and with a slope more different from 1.0 (0.88) for polycyclic compounds. The comparative analysis presented here supports the use of the sumconnectivity index in QSPR/QSAR studies together with the product-connectivity index. Further studies on larger and more heterogeneous datasets should test the sum-connectivity index in QSPR/QSAR models.
Explicit values of multi-dimensional Kloosterman sums for prime powers, II
NASA Astrophysics Data System (ADS)
Gurak, S.
2008-03-01
For any integer m>1 fix zeta_{m}Dexp(2 pi i/m) , and let Z_{m}^{*} denote the group of reduced residues modulo m . Let qDp^{alpha} , a power of a prime p . The hyper-Kloosterman sums of dimension n>0 are defined for q by displaylines{ R(d,q)D sum_{x_{1}, ..., x_{n} in Z_{q}^{*}} ze... ...ots +x_{n} +d(x_{1} \\cdots x_{n})^{-1}} ;;;;;; (d in Z_{q}^{*}), } where x^{-1} denotes the multiplicative inverse of x modulo q . Salie evaluated R(d,q) in the classical setting nD1 for even q , and for odd qDp^{alpha} with alpha >1 . Later, Smith provided formulas that simplified the computation of R(d,q) in these cases for n>1 . Recently, Cochrane, Liu and Zheng computed upper bounds for R(d,q) in the general case n >0 , stopping short of their explicit evaluation. Here I complete the computation they initiated to obtain explicit values for the Kloosterman sums for alpha >1 , relying on basic properties of some simple specialized exponential sums. The treatment here is more elementary than the author's previous determination of these Kloosterman sums using character theory and p -adic methods. At the least, it provides an alternative, independent evaluation of the Kloosterman sums.
The sum-connectivity index--an additive variant of the Randic connectivity index.
Lučić, Bono; Sović, Ivan; Batista, Jadranko; Skala, Karolj; Plavšić, Dejan; Vikić-Topić, Drazen; Bešlo, Drago; Nikolić, Sonja; Trinajstić, Nenad
2013-06-01
This review discusses structure-property modeling applications of a novel variant of the Randic connectivity index that is called the sum-connectivity index. We compare published one-descriptor quantitative structure-property relationship (QSPR) models obtained with the new sum-connectivity index and with the Randic connectivity index, called here the product-connectivity index. Additionally, the efficiency of both variants of connectivity indices in QSPR modeling is tested on five datasets of alkanes and two datasets of polycyclic hydrocarbons. Several physicochemical properties of alkanes (i.e. boiling and melting points, retention index, molar volume, molar refraction, heat of vaporization, standard Gibbs energy of formation, critical temperature, critical pressure, surface tension, density) and π- electronic energies of two sets of polycyclic hydrocarbons were correlated with the product- and sum-connectivity indices. A comparison of these QSPR models shows that both variants of connectivity indices are equivalent, and only slightly (but not significantly) better results are obtained with the sum-connectivity index. Inter-correlations between the product- and sum-connectivity indices are mostly linear with a slope very close to 1.0 for alkanes, and with a slope more different from 1.0 (0.88) for polycyclic compounds. The comparative analysis presented here supports the use of the sumconnectivity index in QSPR/QSAR studies together with the product-connectivity index. Further studies on larger and more heterogeneous datasets should test the sum-connectivity index in QSPR/QSAR models. PMID:23700992
JetSum: SMA actuator based undersea unmanned vehicle inspired by jellyfish bio-mechanics
NASA Astrophysics Data System (ADS)
Bressers, Scott; Chung, Sanghun; Villanueva, Alex; Smith, Colin; Priya, Shashank
2010-04-01
Previously, we reported an undersea unmanned vehicle (UUV) termed as JetSum, inspired by the locomotion of medusa jellyfish, [12]. The propulsion of JetSum was based on shape memory alloy (SMA) wires replicating the contraction-relaxation cycle of natural jellyfish locomotion. In this paper, we report modified design of JetSum that addresses problems related to electrical isolation and power consumption. The modifications lead to significant improvement in functionality, providing implementation of a full continuous bell, bolstering critical sealing junctions, and reducing the overall power requirement. A LabVIEW controller program was developed to automate and optimize the driving of JetSum enabling reduction in power consumption for full contraction of SMA. JetSum locomotion in underwater conditions was recorded by using a high-speed camera and analyzed with image processing techniques developed in MatLab. The results show that JetSum was able to achieve velocity of 7 cm/s with power consumption of 8.94 W per cycle.
A Generalization of the Formula for the Triangular Number of the Sum and Product of Natural Numbers
ERIC Educational Resources Information Center
Asiru, M. A.
2008-01-01
This note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of "r" natural numbers. The formula is applied to derive formula for the sum of an odd and an even number of consecutive triangular numbers.
Revisions to direct fee payment rules. Final rules.
2015-01-01
We are adopting, with two revisions, our interim final rules that implemented amendments to the Social Security Act (Act) made by the Social Security Disability Applicants' Access to Professional Representation Act of 2010 (PRA). The interim final rules made permanent the direct fee payment rules for eligible non-attorney representatives under titles II and XVI of the Act and for attorney representatives under title XVI of the Act. They also revised some of our eligibility policies for non-attorney representatives under titles II and XVI of the Act. Based on public comment and subsequent inquiries, we are revising our rules to clarify that an eligible non-attorney representative's liability insurance policy must include malpractice coverage. We are also reaffirming that a business entity legally permitted to provide the required insurance in the States in which the non-attorney representative conducts business must underwrite the policies.
Universal waste rule: Final rule issued. Environmental Guidance Regulatory Bulletin
1995-08-14
On February 11, 1993, EPA proposed to streamline the management requirements for certain hazardous wastes that were generated in large quantities by a variety of generators (i.e., residential, small businesses, industries, etc.). EPA`s intention was to facilitate the environmentally sound collection and disposal of these types of wastes. In this proposed rule, EPA termed these types of hazardous wastes ``universal wastes`` and developed a management system which was less stringent than the existing Subtitle C regulations. EPA proposed that the following three types of hazardous wastes be managed as universal wastes: batteries, certain pesticides, and thermostats. Because EPA believed that the authority to propose the promulgation of the universal waste rule was not significantly linked to HSWA provisions, the Agency proposed the promulgation of the universal waste rule under pre-HSWA authority. On May 11, 1995, at FR 25492, EPA promulgated a pre-HSWA rule that streamlined hazardous waste management regulations for universal wastes.
A Perspective on Solubility Rules.
ERIC Educational Resources Information Center
Monroe, Manus; Abrams, Karl
1984-01-01
Presents four generalizations about solubilities. These generalizations (rules), are useful in introducing the dynamic topics of solubility and in helping high school and introductory college chemistry students make some order out of the tremendous number of facts available. (JN)
Rule-Based Runtime Verification
NASA Technical Reports Server (NTRS)
Barringer, Howard; Goldberg, Allen; Havelund, Klaus; Sen, Koushik
2003-01-01
We present a rule-based framework for defining and implementing finite trace monitoring logics, including future and past time temporal logic, extended regular expressions, real-time logics, interval logics, forms of quantified temporal logics, and so on. Our logic, EAGLE, is implemented as a Java library and involves novel techniques for rule definition, manipulation and execution. Monitoring is done on a state-by-state basis, without storing the execution trace.
Using the Chain Rule as the Key Link in Deriving the General Rules for Differentiation
ERIC Educational Resources Information Center
Sprows, David
2011-01-01
The standard approach to the general rules for differentiation is to first derive the power, product, and quotient rules and then derive the chain rule. In this short article we give an approach to these rules which uses the chain rule as the main tool in deriving the power, product, and quotient rules in a manner which is more student-friendly…
Rules and Self-Rules: Effects of Variation upon Behavioral Sensitivity to Change
ERIC Educational Resources Information Center
Baumann, Ana A.; Abreu-Rodrigues, Josele; da Silva Souza, Alessandra
2009-01-01
Four experiments compared the effects of self-rules and rules, and varied and specific schedules of reinforcement. Participants were first exposed to either several schedules (varied groups) or to one schedule (specific groups) and either were asked to generate rules (self-rule groups), were provided rules (rule groups), or were not asked nor…
The operator-sum-difference representation of a quantum noise channel
NASA Astrophysics Data System (ADS)
Omkar, S.; Srikanth, R.; Banerjee, Subhashish
2015-06-01
When a model for quantum noise is exactly solvable, a Kraus (or operator-sum) representation can be derived from the spectral decomposition of the Choi matrix for the channel. More generally, a Kraus representation can be obtained from any positive-sum (or ensemble) decomposition of the matrix. Here we extend this idea to any Hermitian-sum decomposition. This yields what we call the "operator-sum-difference" (OSD) representation, in which the channel can be represented as the sum and difference of "subchannels." As one application, the subchannels can be chosen to be analytically diagonalizable, even if the parent channel is not (on account of the Abel-Galois irreducibility theorem), though in this case the number of the OSD representation operators may exceed the channel rank. Our procedure is applicable to general Hermitian (completely positive or non-completely positive) maps and can be extended to the more general, linear maps. As an illustration of the application, we derive an OSD representation for a two-qubit amplitude-damping channel.
The spatial distance rule in the moving and classical rubber hand illusions.
Kalckert, Andreas; Ehrsson, H Henrik
2014-11-01
The rubber hand illusion (RHI) is a perceptual illusion in which participants perceive a model hand as part of their own body. Here, through the use of one questionnaire experiment and two proprioceptive drift experiments, we investigated the effect of distance (12, 27.5, and 43cm) in the vertical plane on both the moving and classical RHI. In both versions of the illusion, we found an effect of distance on ownership of the rubber hand for both measures tested. Our results further suggested that the moving RHI might follow a narrower spatial rule. Finally, whereas ownership of the moving rubber hand was affected by distance, this was not the case for agency, which was present at all distances tested. In sum, the present results generalize the spatial distance rule in terms of ownership to the vertical plane of space and demonstrate that also the moving RHI obeys this rule.
Broadband performance of superdirective delay-and-sum beamformers steered to end-fire.
Trucco, A; Traverso, F; Crocco, M
2014-06-01
Linear arrays steered to end-fire provide superdirective robust performance if a constraint is imposed on the white-noise gain. Filter-and-sum beamformers achieve the maximum constrained directivity by tuning their complex weights over the frequency. Delay-and-sum beamformers have simpler structures, but their weights are fixed and optimized at a given frequency. This letter investigates the constrained directivity provided over a broad band by different delay-and-sum techniques. Complex weights and analytic signals attain near-optimal broadband performance over four octaves. Oversteered arrays using real weights and signals were found to attain superdirective performance over approximately two octaves. Hearing aids and directional hydrophones are potential applications for the considered arrays.
Calculation of Coincidence Summing Correction Factors for an HPGe detector using GEANT4.
Giubrone, G; Ortiz, J; Gallardo, S; Martorell, S; Bas, M C
2016-07-01
The aim of this paper was to calculate the True Coincidence Summing Correction Factors (TSCFs) for an HPGe coaxial detector in order to correct the summing effect as a result of the presence of (88)Y and (60)Co in a multigamma source used to obtain a calibration efficiency curve. Results were obtained for three volumetric sources using the Monte Carlo toolkit, GEANT4. The first part of this paper deals with modeling the detector in order to obtain a simulated full energy peak efficiency curve. A quantitative comparison between the measured and simulated values was made across the entire energy range under study. The True Summing Correction Factors were calculated for (88)Y and (60)Co using the full peak efficiencies obtained with GEANT4. This methodology was subsequently applied to (134)Cs, and presented a complex decay scheme. PMID:27085040
Ab initio investigation of the sum-frequency hyperpolarizability of small chiral molecules
NASA Astrophysics Data System (ADS)
Champagne, Benoı̂t; Fischer, Peer; Buckingham, A. David
2000-11-01
Using a sum-over-states procedure based on configuration interaction singles /6-311++G **, we have computed the sum-frequency hyperpolarizability βijk(-3 ω;2 ω, ω) of two small chiral molecules, R-monofluoro-oxirane and R-(+)-propylene oxide. Excitation energies were scaled to fit experimental UV-absorption data and checked with ab initio values from time-dependent density functional theory. The isotropic part of the computed hyperpolarizabilities, β¯(-3ω;2ω,ω) , is much smaller than that reported previously from sum-frequency generation experiments on aqueous solutions of arabinose. Comparison is made with a single-centre chiral model.
NASA Astrophysics Data System (ADS)
Meng, Xiang-Guo; Wang, Ji-Suo; Gao, Hua-Chao
2016-08-01
Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator M l, m is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ | β> = | β>< β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.
Diode laser pumped green light source based on intracavity sum frequency generation
NASA Astrophysics Data System (ADS)
Fu, X. H.; Che, Y.; Li, Y. L.; Jiang, H. L.
2011-07-01
We report a continuous-wave (CW) green laser emission by sum-frequency mixing in Nd:GdVO4 and Nd:YLF crystals. Using type-I critical phase-matching (CPM) LBO crystal, a green laser at 538 nm is obtained by 912 and 1313 nm intracavity sum-frequency mixing. The maximum output power of 185 mW is obtained when an incident pump laser of 18.2 W is used. At the output power level of 185 mW, the output stability is better than 3.3%.
Metrological activity determination of 133Ba by sum-peak absolute method
NASA Astrophysics Data System (ADS)
da Silva, R. L.; de Almeida, M. C. M.; Delgado, J. U.; Poledna, R.; Santos, A.; de Veras, E. V.; Rangel, J.; Trindade, O. L.
2016-07-01
The National Laboratory for Metrology of Ionizing Radiation provides gamma sources of radionuclide and standardized in activity with reduced uncertainties. Relative methods require standards to determine the sample activity while the absolute methods, as sum-peak, not. The activity is obtained directly with good accuracy and low uncertainties. 133Ba is used in research laboratories and on calibration of detectors for analysis in different work areas. Classical absolute methods don't calibrate 133Ba due to its complex decay scheme. The sum-peak method using gamma spectrometry with germanium detector standardizes 133Ba samples. Uncertainties lower than 1% to activity results were obtained.
Sum-frequency generation of continuous-wave light at 194 nm.
Berkeland, D J; Cruz, F C; Bergquist, J C
1997-06-20
Over 2 mW of continuous-wave tunable 194-nm light is produced by sum-frequency mixing approximately 500 mW of 792-nm and 500 mW of 257-nm radiation in beta-barium borate (BBO). The powers in both fundamental beams are enhanced in separate ring cavities whose optical paths overlap in the Brewster-cut BBO crystal. Due to the higher circulating fundamental powers, the sum-frequency-generated power is nearly 2 orders of magnitude greater than previously reported values.
Measurement of the summed residual projectile mass in relativistic heavy-ion collisions
Stevenson, J.D.; Martinis, J.; Price, P.B.
1981-10-05
Measurements of the summed mass of projectile fragments, M/sub s/ = summationM/sub pf/, are reported for 2.1-GeV/nucleon /sup 20/Ne+C and /sup 20/Ne+Mo. Unlike previous measurements of cross sections for individual projectile fragments, these measurements are quite sensitive to the size of the target nucleus. The distribution of summed residual projectile mass, M/sub s/, provides the first conclusive evidence of the validity of the geometrical ''abrasion'' model of relativistic heavy-ion collisions.
Sum and buffer amplifier for lead-glass barrel calorimeter in the TOPAZ detector
Ujiie, N.; Ikeda, M.; Inaba, S.
1988-02-01
Analog sum and buffer amplifiers have been developed to provide a fast trigger signal from the lead-glass electromagnetic calorimeter in the TOPAZ detector for TRISTAN e/sup +/e/sup -/ collider experiments at KEK. The total kick-back noise from the 4300 channel gate signals of the LeCroy FASTBUS ADC 1885N has been suppressed to less than 40 mV (equivalent to a 0.4 GeV electron signal). The performances of the analog sum and buffer amplifiers that have been developed are described.
Beating photo-degradation in sum-frequency imaging of chiral organic media
NASA Astrophysics Data System (ADS)
Taupier, Grégory; Boeglin, Alex; Crégut, Olivier; Mager, Loïc; Barsella, Alberto; Gąsior, Katarzyna; Rehspringer, Jean-Luc; (Honorat) Dorkenoo, Kokou D.
2015-07-01
Sum-frequency generation from chiral bulk media holds the promise of a powerful tool in the investigation of biological as well as artificial materials containing optically active elements. Since this technique is based on a nonlinear optical effect, the high intensities of the illuminating light sources may induce spurious artifacts. Using simple conjugated chromophores, we demonstrate that multi-photon induced irreversible photolysis may be avoided while keeping undiminished levels of sum-frequency signals. In addition we show that the concurrent multi-photon induced luminescence may provide complementary means of imaging samples.
Primary activity standardization of (57)Co by sum-peak method.
Iwahara, A; Poledna, R; da Silva, C J; Tauhata, L
2009-10-01
The sum-peak method was applied to standardize a (57)Co solution within the framework of an international comparison organized by International Atomic Energy Agency, in 2008, aimed toward international traceability of activity measurements. A planar germanium detector was used with the sources placed on top of the detector for activity determination measurements. An analytical expression for accidental summing correction was derived and the effect of the germanium characteristic KX-ray escape peak of 112keV was taken into account. The standard uncertainty associated to the activity concentration value was 0.37% and the result was compared with other measurement methods. PMID:19505830
Compact 498-nm light source based on intracavity sum-frequency Nd:GGG laser
NASA Astrophysics Data System (ADS)
Wang, A. G.; Li, Y. L.
2011-08-01
We report a coherent cyan radiation at 498 nm by intracavity sum-frequency generation of the 937 and 1062 nm laser-lines of the Nd:GGG crystal. With a diode pump power of 18.2 W, the maximum cyan output power of 186 mW is obtained. The beam quality M2 value is 1.22 in the horizontal plane. The output power stability over 30 min is better than 5%. To the best of our knowledge, this is first work on intracavity sum-frequency generation of a diode pumped Nd:GGG laser at 498 nm.
Experimental validation of coincidence summing corrections computed by the ETNA software.
Lépy, Marie-Christine; Brun, Philippe; Collin, Claude; Plagnard, Johann
2006-01-01
The ETNA software has been developed to compute efficiency transfer and coincidence summing corrections. Different experiments are combined to test the validity of this last facility. Point sources with multi-gamma emitters are measured at several source-to-detector distances. Experimental correction factors are determined from the variation in the peaks' relative intensities versus the geometrical conditions. The ETNA code is used to compute the corrections due to coincidence summing for the same geometries. The calculated values are compared to the experimental ones.
Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function
Linton, C. M.
2015-01-15
A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.
NASA Technical Reports Server (NTRS)
Nieten, Joseph L.; Seraphine, Kathleen M.
1991-01-01
Procedural modeling systems, rule based modeling systems, and a method for converting a procedural model to a rule based model are described. Simulation models are used to represent real time engineering systems. A real time system can be represented by a set of equations or functions connected so that they perform in the same manner as the actual system. Most modeling system languages are based on FORTRAN or some other procedural language. Therefore, they must be enhanced with a reaction capability. Rule based systems are reactive by definition. Once the engineering system has been decomposed into a set of calculations using only basic algebraic unary operations, a knowledge network of calculations and functions can be constructed. The knowledge network required by a rule based system can be generated by a knowledge acquisition tool or a source level compiler. The compiler would take an existing model source file, a syntax template, and a symbol table and generate the knowledge network. Thus, existing procedural models can be translated and executed by a rule based system. Neural models can be provide the high capacity data manipulation required by the most complex real time models.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 16 Commercial Practices 1 2011-01-01 2011-01-01 false The Rule. 429.1 Section 429.1 Commercial Practices FEDERAL TRADE COMMISSION TRADE REGULATION RULES RULE CONCERNING COOLING-OFF PERIOD FOR SALES MADE AT HOMES OR AT CERTAIN OTHER LOCATIONS § 429.1 The Rule. In connection with any door-to-door sale,...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 16 Commercial Practices 1 2010-01-01 2010-01-01 false The Rule. 429.1 Section 429.1 Commercial Practices FEDERAL TRADE COMMISSION TRADE REGULATION RULES RULE CONCERNING COOLING-OFF PERIOD FOR SALES MADE AT HOMES OR AT CERTAIN OTHER LOCATIONS § 429.1 The Rule. In connection with any door-to-door sale,...
75 FR 66709 - Commercial Radio Operators Rules
Federal Register 2010, 2011, 2012, 2013, 2014
2010-10-29
... COMMISSION 47 CFR Parts 0, 1, 13, 80, and 87 Commercial Radio Operators Rules AGENCY: Federal Communications Commission. ACTION: Proposed rule. SUMMARY: This document proposes to amend our rules concerning commercial... within the commercial radio operators service, to determine which rules can be clarified, streamlined,...
76 FR 76815 - Business Opportunity Rule
Federal Register 2010, 2011, 2012, 2013, 2014
2011-12-08
... ``Amended Franchise Rule'' refers to the amended Franchise Rule published at 72 FR 15444 (Mar. 30, 2007) and... Opportunity Ventures: Advanced Notice of Proposed Rulemaking, 62 FR 9115 (Feb. 28, 1997). ``Initial Proposed... Rule, 71 FR 9054 (Apr. 12, 2006). ``Interim Business Opportunity Rule'' refers to the...
Code of Federal Regulations, 2010 CFR
2010-07-01
... 29 Labor 1 2010-07-01 2010-07-01 true Hearsay rule. 18.802 Section 18.802 Labor Office of the Secretary of Labor RULES OF PRACTICE AND PROCEDURE FOR ADMINISTRATIVE HEARINGS BEFORE THE OFFICE OF ADMINISTRATIVE LAW JUDGES Rules of Evidence Hearsay § 18.802 Hearsay rule. Hearsay is not admissible except...
Conformance Testing: Measurement Decision Rules
NASA Technical Reports Server (NTRS)
Mimbs, Scott M.
2010-01-01
The goal of a Quality Management System (QMS) as specified in ISO 9001 and AS9100 is to provide assurance to the customer that end products meet specifications. Measuring devices, often called measuring and test equipment (MTE), are used to provide the evidence of product conformity to specified requirements. Unfortunately, processes that employ MTE can become a weak link to the overall QMS if proper attention is not given to the measurement process design, capability, and implementation. Documented "decision rules" establish the requirements to ensure measurement processes provide the measurement data that supports the needs of the QMS. Measurement data are used to make the decisions that impact all areas of technology. Whether measurements support research, design, production, or maintenance, ensuring the data supports the decision is crucial. Measurement data quality can be critical to the resulting consequences of measurement-based decisions. Historically, most industries required simplistic, one-size-fits-all decision rules for measurements. One-size-fits-all rules in some cases are not rigorous enough to provide adequate measurement results, while in other cases are overly conservative and too costly to implement. Ideally, decision rules should be rigorous enough to match the criticality of the parameter being measured, while being flexible enough to be cost effective. The goal of a decision rule is to ensure that measurement processes provide data with a sufficient level of quality to support the decisions being made - no more, no less. This paper discusses the basic concepts of providing measurement-based evidence that end products meet specifications. Although relevant to all measurement-based conformance tests, the target audience is the MTE end-user, which is anyone using MTE other than calibration service providers. Topics include measurement fundamentals, the associated decision risks, verifying conformance to specifications, and basic measurement
Flight Rules Critical Readiness Review
NASA Technical Reports Server (NTRS)
Kim, E.; Knudsen, F.; Rice, S.
2010-01-01
The increment 23/24 Critical Readiness Review (CRR) flight rules are presented. The topics include: 1) B13-152 Acoustic Constraints; 2) B13-113 IFM/Corrective Action Prioritization Due to Loss of Exercise Capability; 3) B13-116 Constraints on Treadmill VIS Failure; 4) B13-201 Medical Management of ISS Fire/Smoke Response; 5) ARED and T2 Exercise constraints Flight rules (flight and stage specific); 6) FYI: B14 FR to be updated with requirement to sample crew sleep locations prior to receiving a "recommendation" from SRAG on where to sleep.
Rule generation from neural networks
Fu, L.
1994-08-01
The neural network approach has proven useful for the development of artificial intelligence systems. However, a disadvantage with this approach is that the knowledge embedded in the neural network is opaque. In this paper, we show how to interpret neural network knowledge in symbolic form. We lay down required definitions for this treatment, formulate the interpretation algorithm, and formally verify its soundness. The main result is a formalized relationship between a neural network and a rule-based system. In addition, it has been demonstrated that the neural network generates rules of better performance than the decision tree approach in noisy conditions. 7 refs.
Song, Bosheng; Pérez-Jiménez, Mario J; Pan, Linqiang
2015-04-01
P systems are computing models inspired by some basic features of biological membranes. In this work, membrane division, which provides a way to obtain an exponential workspace in linear time, is introduced into (cell-like) P systems with communication (symport/antiport) rules, where objects are never modified but they just change their places. The computational efficiency of this kind of P systems is studied. Specifically, we present a (uniform) linear time solution to the NP-complete problem, Subset Sum by using division rules for elementary membranes and communication rules of length at most 3. We further prove that such P system allowing division rules for non-elementary membranes can efficiently solve the PSPACE-complete problem, QSAT in a uniform way.
Comprehensive Child Welfare Information System. Final rule.
2016-06-01
This final rule replaces the Statewide and Tribal Automated Child Welfare Information Systems (S/TACWIS) rule with the Comprehensive Child Welfare Information System (CCWIS) rule. The rule also makes conforming amendments in rules in related requirements. This rule will assist title IV-E agencies in developing information management systems that leverage new innovations and technology in order to better serve children and families. More specifically, this final rule supports the use of cost-effective, innovative technologies to automate the collection of high-quality case management data and to promote its analysis, distribution, and use by workers, supervisors, administrators, researchers, and policy makers.
Parallel machine architecture for production rule systems
Allen, Jr., John D.; Butler, Philip L.
1989-01-01
A parallel processing system for production rule programs utilizes a host processor for storing production rule right hand sides (RHS) and a plurality of rule processors for storing left hand sides (LHS). The rule processors operate in parallel in the recognize phase of the system recognize -Act Cycle to match their respective LHS's against a stored list of working memory elements (WME) in order to find a self consistent set of WME's. The list of WME is dynamically varied during the Act phase of the system in which the host executes or fires rule RHS's for those rules for which a self-consistent set has been found by the rule processors. The host transmits instructions for creating or deleting working memory elements as dictated by the rule firings until the rule processors are unable to find any further self-consistent working memory element sets at which time the production rule system is halted.
Lower bounds for sums of eigenvalues of elliptic operators and systems
Ilyin, Aleksei A
2013-04-30
Two-term lower bounds of Berzin-Li-Yau type are obtained for the sums of eigenvalues of elliptic operators and systems with constant coefficients and Dirichlet boundary conditions. The polyharmonic operator, the Stokes system and its generalizations, the two-dimensional buckling problem, and also the Klein-Gordon operator are considered. Bibliography: 32 titles.
The Approximation of Two-Mode Proximity Matrices by Sums of Order-Constrained Matrices.
ERIC Educational Resources Information Center
Hubert, Lawrence; Arabie, Phipps
1995-01-01
A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered defines Q-forms for particular conditions in a two-mode matrix. (SLD)
20 CFR 725.521 - Commutation of payments; lump sum awards.
Code of Federal Regulations, 2010 CFR
2010-04-01
....521 Section 725.521 Employees' Benefits EMPLOYMENT STANDARDS ADMINISTRATION, DEPARTMENT OF LABOR.... (f) In the event that an operator or carrier is adjudicated liable for the payment of benefits, such... determine whether a lump sum award shall be made. Such operator or carrier shall, in the event a lump...
Validating Clusters with the Lower Bound for Sum-of-Squares Error
ERIC Educational Resources Information Center
Steinley, Douglas
2007-01-01
Given that a minor condition holds (e.g., the number of variables is greater than the number of clusters), a nontrivial lower bound for the sum-of-squares error criterion in K-means clustering is derived. By calculating the lower bound for several different situations, a method is developed to determine the adequacy of cluster solution based on…
Asymmetries in Responses to Attitude Statements: The Example of "Zero-Sum" Beliefs.
Smithson, Michael; Shou, Yiyun
2016-01-01
While much has been written about the consequences of zero-sum (or fixed-pie) beliefs, their measurement has received almost no systematic attention. No researchers, to our awareness, have examined the question of whether the endorsement of a zero-sum-like proposition depends on how the proposition is formed. This paper focuses on this issue, which may also apply to the measurement of other attitudes. Zero-sum statements have a form such as "The more of resource X for consumer A, the less of resource Y for consumer B." X and Y may be the same resource (such as time), but they can be different (e.g., "The more people commute by bicycle, the less revenue for the city from car parking payments"). These statements have four permutations, and a strict zero-sum believer should regard these four statements as equally valid and therefore should endorse them equally. We find, however, that three asymmetric patterns routinely occur in people's endorsement levels, i.e., clear framing effects, whereby endorsement of one permutation substantially differs from endorsement of another. The patterns seem to arise from beliefs about asymmetric resource flows and power relations between rival consumers. We report three studies, with adult samples representative of populations in two Western and two non-Western cultures, demonstrating that most of the asymmetric belief patterns are consistent across these samples. We conclude with a discussion of the implications of this kind of "order-effect" for attitude measurement. PMID:27445942
5 CFR 831.2005 - Designation of beneficiary for lump-sum payment.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 5 Administrative Personnel 2 2010-01-01 2010-01-01 false Designation of beneficiary for lump-sum payment. 831.2005 Section 831.2005 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED.... (e) A change of beneficiary may be made at any time and without the knowledge or consent of...
The Great Gorilla Jump: An Introduction to Riemann Sums and Definite Integrals
ERIC Educational Resources Information Center
Sealey, Vicki; Engelke, Nicole
2012-01-01
The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…
Some Half-Row Sums from Pascal's Triangle via Laplace Transforms
ERIC Educational Resources Information Center
Dence, Thomas P.
2007-01-01
This article presents some identities on the sum of the entries in the first half of a row in Pascal's triangle. The results were discovered while the author was working on a problem involving Laplace transforms, which are used in proving of the identities.
20 CFR 341.2 - Sum or damages paid or payable.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 341.2 Employees' Benefits RAILROAD RETIREMENT BOARD REGULATIONS UNDER THE RAILROAD UNEMPLOYMENT INSURANCE ACT STATUTORY LIEN WHERE SICKNESS BENEFITS PAID § 341.2 Sum or damages paid or payable. (a) The... or similar insurance policy carried by an employee. (5) Payments made to an employee under the...
Sum-of-Squares Results for Polynomials Related to the Bessis-Moussa-Villani Conjecture
NASA Astrophysics Data System (ADS)
Collins, Benoît; Dykema, Kenneth J.; Torres-Ayala, Francisco
2010-06-01
We show that the polynomial S m, k ( A, B), that is the sum of all words in noncommuting variables A and B having length m and exactly k letters equal to B, is not equal to a sum of commutators and Hermitian squares in the algebra R< X, Y>, where X 2= A and Y 2= B, for all even values of m and k with 6≤ k≤ m-10, and also for ( m, k)=(12,6). This leaves only the case ( m, k)=(16,8) open. This topic is of interest in connection with the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture, which asks whether Tr ( S m, k ( A, B))≥0 holds for all positive semidefinite matrices A and B. These results eliminate the possibility of using "descent + sum-of-squares" to prove the BMV conjecture. We also show that S m,4( A, B) is equal to a sum of commutators and Hermitian squares in R< A, B> when m is even and not a multiple of 4, which implies Tr ( S m,4( A, B))≥0 holds for all Hermitian matrices A and B, for these values of m.
40 CFR 35.910-5 - Additional allotments of previously withheld sums.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 1 2011-07-01 2011-07-01 false Additional allotments of previously withheld sums. 35.910-5 Section 35.910-5 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY GRANTS AND OTHER FEDERAL ASSISTANCE STATE AND LOCAL ASSISTANCE Grants for Construction of Treatment Works-Clean Water Act § 35.910-5 Additional...
ERIC Educational Resources Information Center
Sockloff, Alan L.
1977-01-01
Product correlation was studied under the condition that the original variables are jointly distributed multivariate normal with equal coefficients of variation. Product correlation was shown to range between the two extremes of sum correlation and either the value zero or an unfamiliar function of the intercorrelations of the original variables.…
Support activities to maintain SUMS flight readiness, volume 2. Attachment A: Flight 61-C report
NASA Technical Reports Server (NTRS)
Wright, Willie
1992-01-01
The Shuttle Upper Atmosphere Mass Spectrometer (SUMS), a component experiment of the NASA Orbital Experiments Program (OEX), was flown aboard the shuttle Columbia (OV102) mounted at the forward end of the nose landing gear well with an atmospheric gas inlet system fitted to the lower fuselage (chin panel) surface. The SUMS was designed to provide atmospheric data in flow regimes inaccessible prior to the development of the Space Transportation system (STS). The experiment mission operation begins about 1 hour to shuttle de-orbit entry maneuver and continues until reaching 1.6 torr (about 86 km altitude). The SUMS flew a total of three missions, 61C, STS-35, and STS-40. Between flights, the SUMS was maintained in flight ready status. The flight data has been analyzed by the NASA LaRC Aerothermodynamics Branch. Flight data spectrum plots and reports are presented in the Appendices to the Final Technical Report for NAS1-17399. This volume is the flight data report for flight 61-C.
Müller, Stefan; Regensburger, Georg
2016-01-01
A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community. Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace is a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors). In this work, we extend the theorem, first to "subspace cones" and then to general polyhedral cones and polyhedra. Thereby, we refine Minkowski's and Carathéodory's theorems, two fundamental results in polyhedral geometry. We note that, in general, elementary vectors need not be support-minimal; in fact, they are conformally non-decomposable and form a unique minimal set of conformal generators. Our treatment is mathematically rigorous, but suitable for systems biologists, since we give self-contained proofs for our results and use concepts motivated by metabolic pathway analysis. In particular, we study cones defined by linear subspaces and nonnegativity conditions - like the flux cone - and use them to analyze general polyhedral cones and polyhedra. Finally, we review applications of elementary vectors and conformal sums in metabolic pathway analysis. PMID:27252734
24 CFR 570.513 - Lump sum drawdown for financing of property rehabilitation activities.
Code of Federal Regulations, 2011 CFR
2011-04-01
... property rehabilitation activities. 570.513 Section 570.513 Housing and Urban Development Regulations... rehabilitation activities. Subject to the conditions prescribed in this section, recipients may draw funds from the letter of credit in a lump sum to establish a rehabilitation fund in one or more private...
Shaisultanov, Rashid; Eichler, David
2011-03-15
The dielectric tensor is obtained for a general anisotropic distribution function that is represented as a sum over Legendre polynomials. The result is valid over all of k-space. We obtain growth rates for the Weibel instability for some basic examples of distribution functions.
20 CFR 222.44 - Other relationship determinations for lump-sum payments.
Code of Federal Regulations, 2011 CFR
2011-04-01
... THE RAILROAD RETIREMENT ACT FAMILY RELATIONSHIPS Relationship as Parent, Grandchild, Brother or Sister § 222.44 Other relationship determinations for lump-sum payments. Other claimants will be considered to... 20 Employees' Benefits 1 2011-04-01 2011-04-01 false Other relationship determinations for...
20 CFR 222.44 - Other relationship determinations for lump-sum payments.
Code of Federal Regulations, 2012 CFR
2012-04-01
... THE RAILROAD RETIREMENT ACT FAMILY RELATIONSHIPS Relationship as Parent, Grandchild, Brother or Sister § 222.44 Other relationship determinations for lump-sum payments. Other claimants will be considered to... 20 Employees' Benefits 1 2012-04-01 2012-04-01 false Other relationship determinations for...
20 CFR 222.44 - Other relationship determinations for lump-sum payments.
Code of Federal Regulations, 2010 CFR
2010-04-01
... THE RAILROAD RETIREMENT ACT FAMILY RELATIONSHIPS Relationship as Parent, Grandchild, Brother or Sister § 222.44 Other relationship determinations for lump-sum payments. Other claimants will be considered to... 20 Employees' Benefits 1 2010-04-01 2010-04-01 false Other relationship determinations for...
20 CFR 222.44 - Other relationship determinations for lump-sum payments.
Code of Federal Regulations, 2014 CFR
2014-04-01
... RAILROAD RETIREMENT ACT FAMILY RELATIONSHIPS Relationship as Parent, Grandchild, Brother or Sister § 222.44 Other relationship determinations for lump-sum payments. Other claimants will be considered to have the... 20 Employees' Benefits 1 2014-04-01 2012-04-01 true Other relationship determinations for...
20 CFR 222.44 - Other relationship determinations for lump-sum payments.
Code of Federal Regulations, 2013 CFR
2013-04-01
... RAILROAD RETIREMENT ACT FAMILY RELATIONSHIPS Relationship as Parent, Grandchild, Brother or Sister § 222.44 Other relationship determinations for lump-sum payments. Other claimants will be considered to have the... 20 Employees' Benefits 1 2013-04-01 2012-04-01 true Other relationship determinations for...
26 CFR 1.167(b)-3 - Sum of the years-digits method.
Code of Federal Regulations, 2010 CFR
2010-04-01
... Straight line amount Col. (4)÷ life Straight line reserve Col. (5)− Col. (3) accumulated Jan. 1 Remaining life × average service life Asset balance reduced by salvage Col. (1)× (100%− 6.67%) Current additions reduced by salvage Col (2)× (100%− 6.67%) Salvage realized Sum of the years digits...
Sums and Products of Jointly Distributed Random Variables: A Simplified Approach
ERIC Educational Resources Information Center
Stein, Sheldon H.
2005-01-01
Three basic theorems concerning expected values and variances of sums and products of random variables play an important role in mathematical statistics and its applications in education, business, the social sciences, and the natural sciences. A solid understanding of these theorems requires that students be familiar with the proofs of these…
Killian, E.W.
1997-11-01
A technique has been developed at the Idaho National Engineering Laboratory to sum high resolution gamma-ray pulse spectra from systems with multiple Ge detectors. Lockheed Martin Idaho Technologies Company operates a multi-detector spectrometer configuration at the Stored Waste Examination Pilot Plant facility which is used to characterize the radionuclide contents in waste drums destined for shipment to Waste Isolation Pilot Plant. This summing technique was developed to increase the sensitivity of the system, reduce the count times required to properly quantify the radio-nuclides and provide a more consistent methodology for combining data collected from multiple detectors. In spectrometer systems with multiple detectors looking at non homogeneous waste forms it is often difficult to combine individual spectrum analysis results from each detector to obtain a meaningful result for the total waste container. This is particularly true when the counting statistics in each individual spectrum are poor. The spectrum summing technique adds the spectra collected by each detector into a single spectrum which has better counting statistics than each individual spectrum. A normal spectral analysis program can then be used to analyze the sum spectrum to obtain radio-nuclide values which have smaller errors and do not have to be further manipulated to obtain results for the total waste container. 2 refs., 2 figs.
Peirce's cenopythagorean categories, Merleau-Ponty's chiasmatic entrelacs and Grothendieck's Résumé.
Zalamea, Fernando
2015-12-01
We present Peirce's cenopythagorean categories and Merleau-Ponty's entrelacs and chiasma, as universal phenomenological tools, particularly useful for a better understanding of dynamic, non-classical, non-separated contemporary mathematics. As a case study, we revisit Grothendieck's Résumé, and we explore its extremely rich mathematical, semiotical and phenomenological entanglements. PMID:26247628
An Isotonic Partial Credit Model for Ordering Subjects on the Basis of Their Sum Scores
ERIC Educational Resources Information Center
Ligtvoet, Rudy
2012-01-01
In practice, the sum of the item scores is often used as a basis for comparing subjects. For items that have more than two ordered score categories, only the partial credit model (PCM) and special cases of this model imply that the subjects are stochastically ordered on the common latent variable. However, the PCM is very restrictive with respect…
Asymmetries in Responses to Attitude Statements: The Example of "Zero-Sum" Beliefs.
Smithson, Michael; Shou, Yiyun
2016-01-01
While much has been written about the consequences of zero-sum (or fixed-pie) beliefs, their measurement has received almost no systematic attention. No researchers, to our awareness, have examined the question of whether the endorsement of a zero-sum-like proposition depends on how the proposition is formed. This paper focuses on this issue, which may also apply to the measurement of other attitudes. Zero-sum statements have a form such as "The more of resource X for consumer A, the less of resource Y for consumer B." X and Y may be the same resource (such as time), but they can be different (e.g., "The more people commute by bicycle, the less revenue for the city from car parking payments"). These statements have four permutations, and a strict zero-sum believer should regard these four statements as equally valid and therefore should endorse them equally. We find, however, that three asymmetric patterns routinely occur in people's endorsement levels, i.e., clear framing effects, whereby endorsement of one permutation substantially differs from endorsement of another. The patterns seem to arise from beliefs about asymmetric resource flows and power relations between rival consumers. We report three studies, with adult samples representative of populations in two Western and two non-Western cultures, demonstrating that most of the asymmetric belief patterns are consistent across these samples. We conclude with a discussion of the implications of this kind of "order-effect" for attitude measurement.
Law and the Zero-Sum Game of Discrimination: Commentary on Norton and Sommers (2011).
Plaut, Victoria C
2011-05-01
Norton and Sommers (2011, this issue) find that Whites see discrimination as a zero-sum game that they are now losing. This psychological finding has serious implications for antidiscrimination law. This commentary briefly traces the relevant, recent history of antidiscrimination law and explains the consequences of the zero-sum finding in three related areas: affirmative action, disparate treatment, and disparate impact. In all three areas, the zero-sum finding-and the presumption of intentional discrimination against Whites that it indicates-upsets the structure of antidiscrimination law traditionally designed to remedy discrimination against historically disadvantaged racial minorities. Moreover, the zero-sum finding suggests that recent ballot initiatives banning affirmative action and recent, pivotal Supreme Court opinions limiting antidiscrimination laws that were originally erected to prevent the exclusion of racial minorities are not just the product of voters in a handful of states, of a few disgruntled White employees or university applicants, or of a few justices, but rather are reflective of a more widespread societal sentiment. PMID:26168513
A Valuable Experience for Children: The Dim Sum and Chinese Restaurant Project
ERIC Educational Resources Information Center
Ha, Yuen Lai
2010-01-01
This article describes the Dim Sum and Chinese Restaurant Project undertaken by 6-year-old kindergarten children in Hong Kong. The article discusses the importance of listening, observing, and documenting children's actions to meet their needs and interests. The kindergarten program that participated in this project is a nonprofit kindergarten…
Federal Register 2010, 2011, 2012, 2013, 2014
2010-11-29
... AFFAIRS Agency Information Collection (Claim for One Sum Payment (Government Life Insurance)) Activities... Insurance), VA Form 29-4125. b. Claim for Monthly Payments (National Service Life Insurance), VA Form 29-4125a. c. Claim for Monthly Payments (United States Government Life Insurance, (USGLI)), VA Form...
ERIC Educational Resources Information Center
Whitacre, Ian
2015-01-01
This study investigated the sets of mental computation strategies used by prospective elementary teachers to compute sums and differences of whole numbers. In the context of an intervention designed to improve the number sense of prospective elementary teachers, participants were interviewed pre/post, and their mental computation strategies were…
A Repetitive Branch-and-Bound Procedure for Minimum Within-Cluster Sums of Squares Partitioning
ERIC Educational Resources Information Center
Brusco, Michael J.
2006-01-01
Minimization of the within-cluster sums of squares (WCSS) is one of the most important optimization criteria in cluster analysis. Although cluster analysis modules in commercial software packages typically use heuristic methods for this criterion, optimal approaches can be computationally feasible for problems of modest size. This paper presents a…
Sub-15fs ultraviolet pulses generated by achromatic phase-matching sum-frequency mixing.
Zhao, Baozhen; Jiang, Yongliang; Sueda, Keiich; Miyanaga, Noriaki; Kobayashi, Takayoshi
2009-09-28
A broadband ultraviolet pulse with a spectral width of 44 nm was generated by achromatic sum-frequency mixing of an 805-nm pulse and ultrabroadband visible pulse. Angular dispersion was introduced to achieve broadband phase matching by a prism pair. The UV pulse was compressed to 13.2 fs with another prism pair, with energy of 600 nJ. PMID:19907556
40 CFR 35.910-5 - Additional allotments of previously withheld sums.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 1 2012-07-01 2012-07-01 false Additional allotments of previously withheld sums. 35.910-5 Section 35.910-5 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY GRANTS AND OTHER FEDERAL ASSISTANCE STATE AND LOCAL ASSISTANCE Grants for Construction of Treatment Works-Clean Water Act § 35.910-5 Additional...
ERIC Educational Resources Information Center
Green, Samuel B.; Yang, Yanyun
2009-01-01
A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of…
Müller, Stefan; Regensburger, Georg
2016-01-01
A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community. Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace is a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors). In this work, we extend the theorem, first to “subspace cones” and then to general polyhedral cones and polyhedra. Thereby, we refine Minkowski's and Carathéodory's theorems, two fundamental results in polyhedral geometry. We note that, in general, elementary vectors need not be support-minimal; in fact, they are conformally non-decomposable and form a unique minimal set of conformal generators. Our treatment is mathematically rigorous, but suitable for systems biologists, since we give self-contained proofs for our results and use concepts motivated by metabolic pathway analysis. In particular, we study cones defined by linear subspaces and nonnegativity conditions — like the flux cone — and use them to analyze general polyhedral cones and polyhedra. Finally, we review applications of elementary vectors and conformal sums in metabolic pathway analysis. PMID:27252734
5 CFR 847.702 - Lump-sum payments and refunds.
Code of Federal Regulations, 2010 CFR
2010-01-01
... chapter. (b) Government contributions which are transferred to the Fund under subpart E of this part are... Section 847.702 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT (CONTINUED) CIVIL SERVICE... subpart E of this part are included in any lump-sum credit or unexpended balance payable to the...
Detection and Diagnosis of Person Misfit from Patterns of Summed Polytomous Item Scores
ERIC Educational Resources Information Center
Emons, Wilco H. M.
2009-01-01
For valid decision making, it is essential to both the person being measured and the person or organization that is having the person measured that the observed scores adequately represent the underlying trait. This study deals with person-fit analysis of polytomous item scores to detect unusual patterns of sum scores on subsets of items. This…
24 CFR 84.82 - Provisions applicable only to lump sum grants.
Code of Federal Regulations, 2010 CFR
2010-04-01
... INSTITUTIONS OF HIGHER EDUCATION, HOSPITALS, AND OTHER NON-PROFIT ORGANIZATIONS Use of Lump Sum Grants § 84.82... other non-profit organizations (including hospitals) shall be subject to the audit requirements..., “Audits of States, Local Governments, and Non-Profit Organizations.” (i) Non-profit organizations......